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Journal articles on the topic 'Locally compact abelian group'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Székelyhidi, László. "Harmonic Synthesis on Group Extensions." Mathematics 12, no. 19 (2024): 3013. http://dx.doi.org/10.3390/math12193013.

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Harmonic synthesis describes translation invariant linear spaces of continuous complex valued functions on locally compact abelian groups. The basic result due to L. Schwartz states that such spaces on the reals are topologically generated by the exponential monomials in the space; in other words, the locally compact abelian group of the reals is synthesizable. This result does not hold for continuous functions in several real variables, as was shown by D.I. Gurevich’s counterexamples. On the other hand, if two discrete abelian groups have this synthesizability property, then so does their dir

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2

Hossein, Sahleh, and Akbar Alijani Ali. "Extensions of Locally Compact Abelian, Torsion-Free Groups by Compact Torsion Abelian Groups." British Journal of Mathematics & Computer Science 22, no. 4 (2017): 1–5. https://doi.org/10.9734/BJMCS/2017/32966.

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Let <em>X</em> be a compact torsion abelian group. In this paper, we show that an extension of <em>F<sub>p</sub></em> by <em>X</em> splits where <em>F<sub>p</sub></em> is the p-adic number group and p a prime number. Also, we show that an extension of a torsion-free, non-divisible LCA group by <em>X</em> is not split.

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3

Cleary, Joan, and Sidney A. Morris. "Topologies on locally compact groups." Bulletin of the Australian Mathematical Society 38, no. 1 (1988): 105–11. http://dx.doi.org/10.1017/s0004972700027313.

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Using the Iwasawa structure theorem for connected locally compact Hausdorff groups we show that every locally compact Hausdorff group G is homeomorphic to Rn × K × D, where n is a non-negative integer, K is a compact group and D is a discrete group. This makes recent results on cardinal numbers associated with the topology of locally compact groups more transparent. For abelian G, we note that the dual group, Ĝ, is homeomorphic to This leads us to the relationship card G = ω0(Ĝ) + 2ω0(G), where ω (respectively, ω0) denotes the weight (respectively local weight) of the topological group. From t

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4

Morris, Sidney A. "Locally compact topologies on abelian groups." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 2 (1987): 233–35. http://dx.doi.org/10.1017/s0305004100066585.

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AbstractIt is shown that an abelian group admits a non-discrete locally compact group topology if and only if it has a subgroup algebraically isomorphic to the group of p-adic integers or to an infinite product of non-trivial finite cyclic groups. It is also proved that an abelian group admits a non-totally-disconnected locally compact group topology if and only if it has a subgroup algebraically isomorphic to the group of real numbers. Further, if an abelian group admits one non-totally-disconnected locally compact group topology then it admits a continuum of such topologies, no two of which

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5

Bavuma, Yanga, and Francesco G. Russo. "Embeddings of locally compact abelian p-groups in Hawaiian groups." Forum Mathematicum 34, no. 1 (2021): 97–114. http://dx.doi.org/10.1515/forum-2021-0085.

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Abstract We show that locally compact abelian p-groups can be embedded in the first Hawaiian group on a compact path connected subspace of the Euclidean space of dimension four. This result gives a new geometric interpretation for the classification of locally compact abelian groups which are rich in commuting closed subgroups. It is then possible to introduce the idea of an algebraic topology for topologically modular locally compact groups via the geometry of the Hawaiian earring. Among other things, we find applications for locally compact groups which are just noncompact.

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6

Xi, Wenfei, Dikran Dikranjan, Menachem Shlossberg, and Daniele Toller. "Hereditarily minimal topological groups." Forum Mathematicum 31, no. 3 (2019): 619–46. http://dx.doi.org/10.1515/forum-2018-0066.

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Abstract We study locally compact groups having all subgroups minimal. We call such groups hereditarily minimal. In 1972 Prodanov proved that the infinite hereditarily minimal compact abelian groups are precisely the groups {\mathbb{Z}_{p}} of p-adic integers. We extend Prodanov’s theorem to the non-abelian case at several levels. For infinite hypercentral (in particular, nilpotent) locally compact groups, we show that the hereditarily minimal ones remain the same as in the abelian case. On the other hand, we classify completely the locally compact solvable hereditarily minimal groups, showing

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7

Takahashi, Yuji. "Character-pure locally compact abelian groups and their dual groups." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 2 (1990): 311–15. http://dx.doi.org/10.1017/s0305004100069176.

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AbstractWe give some characterizations of the class of character-pure locally compact abelian groups. As an application we supplement a result of Venkataraman characterizing the class of locally compact abelian groups which are topologically pure in their Bohr compactifications. We also study the class of locally compact abelian groups which are pure closed in their Bohr compactifications.

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8

Thomsen, Klaus. "Ergodic actions of group extensions on von Neumann algebras." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 112, no. 1-2 (1989): 71–112. http://dx.doi.org/10.1017/s0308210500028183.

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SynopsisWe consider automorphic actions on von Neumann algebras of a locally compact group E given as a topological extension 0 → A → E → G → 0, where A is compact abelian and second countable. Motivated by the wish to describe and classify ergodic actions of E when G is finite, we classify (up to conjugacy) first the ergodic actions of locally compact groups on finite-dimensional factors and then compact abelian actions with the property that the fixed-point algebra is of type I with atomic centre. We then handle the case of ergodic actions of E with the property that the action is already er

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9

DIKRANJAN, DIKRAN, ANNA GIORDANO BRUNO, and FRANCESCO G. RUSSO. "FINITENESS OF TOPOLOGICAL ENTROPY FOR LOCALLY COMPACT ABELIAN GROUPS." Glasgow Mathematical Journal 63, no. 1 (2020): 81–105. http://dx.doi.org/10.1017/s0017089520000038.

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AbstractWe study the locally compact abelian groups in the class ${\mathfrak E_{ \lt \infty }}$ , that is, having only continuous endomorphisms of finite topological entropy, and in its subclass $\mathfrak E_0$ , that is, having all continuous endomorphisms with vanishing topological entropy. We discuss the reduction of the problem to the case of periodic locally compact abelian groups, and then to locally compact abelian p-groups. We show that locally compact abelian p-groups of finite rank belong to ${\mathfrak E_{ \lt \infty }}$ , and that those of them that belong to $\mathfrak E_0$ are pr

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10

Bloom, Walter R., and Joseph F. Sussich. "Saturation on locally compact abelian groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 2 (1985): 255–67. http://dx.doi.org/10.1017/s1446788700023119.

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AbstractLet G be a locally compact abeian group, (μρ) a net of bounded Radon measures on G. In this paper we consider conditions under which (μρ) is saturated in Lp (G) and apply these results to the Fejér and Picard approximation processes.

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11

Herfort, Wolfgang, Karl H. Hofmann, and Francesco G. Russo. "Locally compact abelian p-groups." Topology and its Applications 259 (June 2019): 203–41. http://dx.doi.org/10.1016/j.topol.2019.02.031.

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12

Dikranjan, Dikran, and Dmitri Shakhmatov. "Characterizing Lie groups by controlling their zero-dimensional subgroups." Forum Mathematicum 30, no. 2 (2018): 295–320. http://dx.doi.org/10.1515/forum-2017-0010.

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AbstractWe provide characterizations of Lie groups as compact-like groups in which all closed zero-dimensional metric (compact) subgroups are discrete. The “compact-like” properties we consider include (local) compactness, (local) ω-boundedness, (local) countable compactness, (local) precompactness, (local) minimality and sequential completeness. Below is A sample of our characterizations is as follows:(i) A topological group is a Lie group if and only if it is locally compact and has no infinite compact metric zero-dimensional subgroups.(ii) An abelian topological groupGis a Lie group if and

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13

Hofmann, Karl Heinrich. "Arc components in locally compact groups are Borel sets." Bulletin of the Australian Mathematical Society 65, no. 1 (2002): 1–8. http://dx.doi.org/10.1017/s0004972700020001.

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Are the arc components in a locally compact group Borel subsets? An affirmative answer is provide for locally compact groups satisfying the First Axiom of Count-ability. For general locally compact groups the question is reduced to compact connected Abelian groups. In certain models of set theory the answer is negative.

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14

Artusa, Marco. "Duality for condensed cohomology of the Weil group of a $p$-adic field." Documenta Mathematica 29, no. 6 (2024): 1381–434. http://dx.doi.org/10.4171/dm/977.

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We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a p -adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This allows us to enlarge the local Tate duality to a more general category of non-necessarily discrete coefficients, where it takes the form of a Pontryagin duality between locally compact abelian groups.

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15

Farhadi, Hamid-Reza. "Isomorphisms between the second duals of group algebras of locally compact groups." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 4 (1996): 657–63. http://dx.doi.org/10.1017/s0305004100074491.

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AbstractLet G be a locally compact group and L1(G) be the group algebra of G. We show that G is abelian or compact if every continuous automorphism of L1(G)** maps L1(G) onto L1(G) This characterizes all groups with this property and answers a question raised by F. Ghahramani and A. T. Lau in [7]. We also show that if G is a compact group and θ is any (algebra) isomorphism from L1(G)** onto L1(H)**, then H is compact and θ maps L1(G) onto L1(H).

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16

Peng, Dekui, Wei He, Mikhail Tkachenko, and Zhiqiang Xiao. "Successors of locally compact topological group topologies on abelian groups." Fundamenta Mathematicae 249, no. 1 (2020): 71–93. http://dx.doi.org/10.4064/fm680-6-2019.

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17

Galindo, Jorge. "Relations between Locally Compact Abelian Groups with Isomorphic Group Algebras." Journal of the London Mathematical Society 61, no. 1 (2000): 110–22. http://dx.doi.org/10.1112/s002461079900811x.

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18

Mahapatra, Prasadini, and Divya Singh. "Scaling sets and generalized scaling sets on Cantor dyadic group." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 04 (2020): 2050019. http://dx.doi.org/10.1142/s0219691320500198.

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Scaling and generalized scaling sets determine wavelet sets and hence wavelets. In real case, wavelet sets were proved to be an important tool for the construction of MRA as well as non-MRA wavelets. However, any result related to scaling/generalized scaling sets is not available in case of locally compact abelian groups. This paper gives a characterization of scaling sets and its generalized version along with relevant examples in dual Cantor dyadic group [Formula: see text]. These results can further be generalized to arbitrary locally compact abelian groups.

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19

Font, Juan J., and Salvador Hernández. "Algebraic characterizations of locally compact groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 62, no. 3 (1997): 405–20. http://dx.doi.org/10.1017/s1446788700001099.

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AbstractLet G1, G2 be locally compact real-compact spaces. A linear map T defined from C(G1) into C(G2) is said to be separating or disjointness preserving if f = g ≡ 0 implies Tf = Tg ≡ 0 f or all f, g ∈ C(G1). In this paper we prove that both a separating map which preserves non-vanishing functions and a separating bijection which satisfies condition (M) (see Definition 4) are automatically continuous and can be written as weighted composition maps. We also study the effect of separating surjections (respectively injections) on the underlying spaces G1 and G2.Next we apply the above results

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20

DE BEER, RICHARD J. "TAUBERIAN THEOREMS AND SPECTRAL THEORY IN TOPOLOGICAL VECTOR SPACES." Glasgow Mathematical Journal 55, no. 3 (2013): 511–32. http://dx.doi.org/10.1017/s0017089512000699.

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AbstractWe investigate the spectral theory of integrable actions of a locally compact abelian group on a locally convex vector space. We start with an analysis of various spectral subspaces induced by the action of the group. This is applied to analyse the spectral theory of operators on the space, generated by measures on the group. We apply these results to derive general Tauberian theorems that apply to arbitrary locally compact abelian groups acting on a large class of locally convex vector spaces, which includes Fréchet spaces. We show how these theorems simplify the derivation of Mean Er

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21

Parthasarathy, K., and Sujatha Varma. "On weak spectral synthesis." Bulletin of the Australian Mathematical Society 43, no. 2 (1991): 279–82. http://dx.doi.org/10.1017/s0004972700029063.

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Weak spectral synthesis fails in the group algebra and the generalised group algebra of any non compact locally compact abelian group and also in the Fourier algebra of any infinite compact Lie group.

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22

Kryuchkov, N. I. "Generalized Cotorsion Locally Compact Abelian Groups." Rendiconti del Seminario Matematico della Università di Padova 127 (2012): 107–20. http://dx.doi.org/10.4171/rsmup/127-7.

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23

Elqorachi, E., M. Akkouchi, A. Bakali, and B. Bouikhalene. "Badora's Equation on Non-Abelian Locally Compact Groups." gmj 11, no. 3 (2004): 449–66. http://dx.doi.org/10.1515/gmj.2004.449.

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Abstract This paper is mainly concerned with the following functional equation where 𝐺 is a locally compact group, 𝐾 a compact subgroup of its morphisms, and μ is a generalized Gelfand measure. It is shown that continuous and bounded solutions of this equation can be expressed in terms of μ-spherical functions. This extends the previous results obtained by Badora (Aequationes Math. 43: 72–89, 1992) on locally compact abelian groups. In the case where 𝐺 is a connected Lie group, we characterize solutions of the equation in question as joint eigenfunctions of certain operators associated to the

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24

Filali, M. "The uniform compactification of a locally compact abelian group." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 3 (1990): 527–38. http://dx.doi.org/10.1017/s0305004100069413.

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In recent years, the Stone-Čech compactification of certain semigroups (e.g. discrete semigroups) has been an interesting semigroup compactification (i.e. a compact right semitopological semigroup which contains a dense continuous homomorphic image of the given semigroup) to study, because an Arens-type product can be introduced. If G is a non-compact and non-discrete locally compact abelian group, then it is not possible to introduce such a product into the Stone-Čech compactification βG of G (see [1]). However, let UC(G) be the Banach algebra of bounded uniformly continuous complex functions

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25

Mehdipour, Mohammad Javad, and Zahra Saeedi. "Derivations on group algebras of a locally compact abelian group." Monatshefte für Mathematik 180, no. 3 (2015): 595–605. http://dx.doi.org/10.1007/s00605-015-0800-1.

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26

KAMYABI GOL, R. A., and R. RAISI TOUSI. "A RANGE FUNCTION APPROACH TO SHIFT-INVARIANT SPACES ON LOCALLY COMPACT ABELIAN GROUPS." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 01 (2010): 49–59. http://dx.doi.org/10.1142/s0219691310003365.

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This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L2(G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Riesz bases generated by shifts of a countable set of generators from L2(ℝn) to L2(G).

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27

Sahleh, Hossein, and Ali Alijani. "Extensions of Locally Compact Abelian, Torsion-Free Groups by Compact Torsion Abelian Groups." British Journal of Mathematics & Computer Science 22, no. 4 (2017): 1–5. http://dx.doi.org/10.9734/bjmcs/2017/32966.

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28

Khan, M. A. "When are dense subgroups of LCA groups closed under intersections?" Bulletin of the Australian Mathematical Society 49, no. 1 (1994): 59–67. http://dx.doi.org/10.1017/s0004972700016087.

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Let G be a nondiscrete locally compact Hausdorff abelian group. It is shown that if G contains an open torsion subgroup, then every proper dense subgroup of G is contained in a maximal subgroup; while if G has no open torsion subgroup, then it has a dense subgroup D such that G/D is algebraically isomorphic to R, the additive group of reals. With each G, containing an open torsion subgroup, we associate the least positive integer n such that the nth multiple of every discontinuous character of G is continuous. The following are proved equivalent for a nondiscrete locally compact abelian group

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29

NASSERDDINE, WASSIM. "A COMPACT QUALITATIVE UNCERTAINTY PRINCIPLE FOR SOME NONUNIMODULAR GROUPS." Bulletin of the Australian Mathematical Society 99, no. 1 (2018): 114–20. http://dx.doi.org/10.1017/s0004972718001119.

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Let $G$ be a separable locally compact group with type $I$ left regular representation, $\widehat{G}$ its dual, $A(G)$ its Fourier algebra and $f\in A(G)$ with compact support. If $G=\mathbb{R}$ and the Fourier transform of $f$ is compactly supported, then, by a classical Paley–Wiener theorem, $f=0$. There are extensions of this theorem for abelian and some unimodular groups. In this paper, we prove that if $G$ has no (nonempty) open compact subsets, $\hat{f}$, the regularised Fourier cotransform of $f$, is compactly supported and $\text{Im}\,\hat{f}$ is finite dimensional, then $f=0$. In conn

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30

Willis, George. "The continuity of derivations from group algebras: factorizable and connected groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 52, no. 2 (1992): 185–204. http://dx.doi.org/10.1017/s1446788700034340.

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AbstractA group is said to be factorizable if it has a finite number of abelian subgroups, H1, H2, … Hn, such that G = H1H2 … Hn. It is shown that, if G is a factorizable or connected locally compact group, then every derivation from L1 (G) to an arbitrary L1 (G)-bimodule X is continuous.

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31

Hofmann, Karl H., Sidney A. Morris, Sheila Oates-Williams, and V. N. Obraztsov. "Locally compact groups with closed subgroups open and p-adic." Mathematical Proceedings of the Cambridge Philosophical Society 118, no. 2 (1995): 303–13. http://dx.doi.org/10.1017/s0305004100073655.

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An open subgroup U of a topological group G is always closed, since U is the complement of the open set . An arbitrary closed subgroup C of G is almost never open, unless G belongs to a small family of exceptional groups. In fact, if G is a locally compact abelian group in which every non-trivial subgroup is open, then G is the additive group δp of p-adic integers or the additive group Ωp of p-adic rationale (cf. Robertson and Schreiber[5[, proposition 7). The fact that δp has interesting properties as a topological group has many roots. One is that its character group is the Prüfer group ℤp∞,

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32

CAPRACE, PIERRE-EMMANUEL, and NICOLAS MONOD. "Decomposing locally compact groups into simple pieces." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 1 (2010): 97–128. http://dx.doi.org/10.1017/s0305004110000368.

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AbstractWe present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic cocompact subgroup which is either connected or admits a non-compact non-discrete topologically simple quotient. We also provide a description of characteristically simple groups and of groups all of whose proper quotients are compact. We show that Noetherian locally compact groups without infinite discrete quotient admit a subnormal series with all s

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33

Alijani, A. A., and A. Yekrangi. "Splitting of Closed Subgroups of Locally Compact Abelian Groups." New Zealand Journal of Mathematics 48 (December 31, 2018): 115–19. http://dx.doi.org/10.53733/32.

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Let £ be the category of all locally compact abelian (LCA) groups. In this paper, we investigate the splitting of the identity component, the subgroup of all compact elements and the maximal torsion subgroup of a group £. A group £ will be called split full if every closed subgroup of G splits. In this paper, we give a necessary condition for an LCA group to be split full.

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34

COONEY, TOM. "A HAUSDORFF–YOUNG INEQUALITY FOR LOCALLY COMPACT QUANTUM GROUPS." International Journal of Mathematics 21, no. 12 (2010): 1619–32. http://dx.doi.org/10.1142/s0129167x10006677.

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Let G be a locally compact abelian group with dual group Ĝ. The Hausdorff–Young theorem states that if f ∈ Lp(G), where 1 ≤ p ≤ 2, then its Fourier transform [Formula: see text] belongs to Lq(Ĝ) (where (1/p) + (1/q) = 1) and [Formula: see text]. Kunze and Terp extended this to unimodular and locally compact groups, respectively. We further generalize this result to an arbitrary locally compact quantum group 𝔾 by defining a Fourier transform [Formula: see text] and showing that this Fourier transform satisfies the Hausdorff–Young inequality.

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35

Jakobsen, Mads Sielemann, and Jakob Lemvig. "Co-compact Gabor Systems on Locally Compact Abelian Groups." Journal of Fourier Analysis and Applications 22, no. 1 (2015): 36–70. http://dx.doi.org/10.1007/s00041-015-9407-0.

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36

Itô, Masayuki, and Noriaki Suzuki. "The semi-balayability of real convolution kernels." Nagoya Mathematical Journal 99 (September 1985): 89–110. http://dx.doi.org/10.1017/s0027763000021516.

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ALAGHMANDAN, MAHMOOD. "APPROXIMATE AMENABILITY OF SEGAL ALGEBRAS." Journal of the Australian Mathematical Society 95, no. 1 (2013): 20–35. http://dx.doi.org/10.1017/s1446788713000256.

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AbstractIn this paper we first show that for a locally compact amenable group $G$, every proper abstract Segal algebra of the Fourier algebra on $G$ is not approximately amenable; consequently, every proper Segal algebra on a locally compact abelian group is not approximately amenable. Then using the hypergroup generated by the dual of a compact group, it is shown that all proper Segal algebras of a class of compact groups including the $2\times 2$ special unitary group, $\mathrm{SU} (2)$, are not approximately amenable.

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38

Leiderman, Arkady, and Mikhail Tkachenko. "Separable Quotients of Free Topological Groups." Canadian Mathematical Bulletin 63, no. 3 (2019): 610–23. http://dx.doi.org/10.4153/s0008439519000699.

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AbstractWe study the following problem: For which Tychonoff spaces $X$ do the free topological group $F(X)$ and the free abelian topological group $A(X)$ admit a quotient homomorphism onto a separable and nontrivial (i.e., not finitely generated) group? The existence of the required quotient homomorphisms is established for several important classes of spaces $X$, which include the class of pseudocompact spaces, the class of locally compact spaces, the class of $\unicode[STIX]{x1D70E}$-compact spaces, the class of connected locally connected spaces, and some others.We also show that there exis

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39

Platonov, Sergey S. "Spectral synthesis on zero-dimensional locally compact Abelian groups." Russian Universities Reports. Mathematics, no. 128 (2019): 450–56. http://dx.doi.org/10.20310/2686-9667-2019-24-128-450-456.

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Let G be a zero-dimensional locally compact Abelian group whose elements are compact, C(G) the space of continuous complex-valued functions on the group G. A closed linear subspace H⊆ C(G) is called invariant subspace, if it is invariant with respect to translations τ_y ∶ f(x) ↦ f(x + y), y ∈ G. We prove that any invariant subspace H admits spectral synthesis, which means that H coincides with the closure of the linear span of all characters of the group G contained in H.

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40

Gordon, E. I. "Nonstandard analysis and locally compact Abelian groups." Acta Applicandae Mathematicae 25, no. 3 (1991): 221–39. http://dx.doi.org/10.1007/bf00047004.

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41

GÓRKA, PRZEMYSłAW. "PEGO THEOREM ON LOCALLY COMPACT ABELIAN GROUPS." Journal of Algebra and Its Applications 13, no. 04 (2014): 1350143. http://dx.doi.org/10.1142/s0219498813501430.

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In this paper, we show the version of Pego's theorem on locally compact abelian groups. This theorem, [R. L. Pego, Compactness in L2 and the Fourier transform, Proc. Amer. Math. Soc.95 (1985) 252–254], gives a characterization of precompact sets of L2 in terms of the Fourier transform.

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42

Keyantuo, Valentin, and Yevhen Zelenyuk. "Semigroup completions of locally compact Abelian groups." Topology and its Applications 263 (August 2019): 199–208. http://dx.doi.org/10.1016/j.topol.2019.06.036.

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43

Rashidi-Kouchi, Mehdi. "Wavelet Sets on Locally Compact Abelian Groups." Mathematical Researches 6, no. 3 (2020): 393–404. http://dx.doi.org/10.52547/mmr.6.3.393.

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44

Hoffmann, Norbert, and Markus Spitzweck. "Homological algebra with locally compact abelian groups." Advances in Mathematics 212, no. 2 (2007): 504–24. http://dx.doi.org/10.1016/j.aim.2006.09.019.

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45

Barczy, Mátyás, Alexander Bendikov, and Gyula Pap. "Limit theorems on locally compact Abelian groups." Mathematische Nachrichten 281, no. 12 (2008): 1708–27. http://dx.doi.org/10.1002/mana.200510709.

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46

Gorin, E. A., and S. Norvidas. "Universal symbols on locally compact Abelian groups." Functional Analysis and Its Applications 47, no. 1 (2013): 1–13. http://dx.doi.org/10.1007/s10688-013-0001-4.

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47

Farkov, Yu A. "Orthogonal wavelets on locally compact Abelian groups." Functional Analysis and Its Applications 31, no. 4 (1997): 294–96. http://dx.doi.org/10.1007/bf02466067.

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Antoniou, I., and S. A. Shkarin. "Decay measures on locally compact abelian topological groups." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 6 (2001): 1257–73. http://dx.doi.org/10.1017/s0308210500001384.

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We show that the Banach space M of regular σ-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces MD and MND, where MD is the set of measures μ ∈ M whose Fourier transform vanishes at infinity and MND is the set of measures μ ∈ M such that ν ∉ MD for any ν ∈ M {0} absolutely continuous with respect to the variation |μ|. For any corresponding decomposition μ = μD + μND (μD ∈ MD and μND ∈ MND) there exist a Borel set A = A(μ) such that μD is the restriction of μ to A, therefore the mea

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Eryilmaz, Ilker, and Cenap Duyar. "On Multipliers of the Group Lp;w(G)-Algebras." Annals of the Alexandru Ioan Cuza University - Mathematics 59, no. 2 (2013): 253–68. http://dx.doi.org/10.2478/v10157-012-0045-4.

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Abstract Let G be a locally compact abelian group (non-compact, non-discrete) with Haar measure and 1 ≤ p < ∞: The purpose of this paper is to study the space of multipliers on Lp;w (G) and characterize it as the algebra of all multipliers of the closely related Banach algebra of tempered elements in Lp;w (G).

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50

Dixit, M. M., C. P. Pandey, and Pratima Devi. "Wavelet frames in Sobolev space over locally compact abelian group." Boletim da Sociedade Paranaense de Matemática 42 (May 8, 2024): 1–11. http://dx.doi.org/10.5269/bspm.65621.

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In this paper we construct wavelet frames for continuous and discrete wavelets on Sobolev space over abelian group. A necessary condition and sufficient conditions for wavelet frames in Sobolev space over Locally CompactAbelian Group are given. Moreover some important properties of continuous wavelet transform and corresponding wavelet Frames have been discussed

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