Relevant bibliographies by topics / Locally compact abelian group

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Academic literature on the topic 'Locally compact abelian group'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Locally compact abelian group"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Locally compact abelian group"

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Gaebler, David. "Toeplitz Operators on Locally Compact Abelian Groups." Scholarship @ Claremont, 2004. https://scholarship.claremont.edu/hmc_theses/163.

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Given a function (more generally, a measure) on a locally compact Abelian group, one can define the Toeplitz operators as certain integral transforms of functions on the dual group, where the kernel is the Fourier transform of the original function or measure. In the case of the unit circle, this corresponds to forming a matrix out of the Fourier coefficients in a particular way. We will study the asymptotic eigenvalue distributions of these Toeplitz operators.
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Yang, Qingde. "Multiresolution analysis on non-abelian locally compact groups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0018/NQ43523.pdf.

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Mattsson, Tobias. "Abstract Harmonic Analysis on Locally Compact Abelian Groups." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354740.

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Cotton, Michael R. "Abelian Group Actions and Hypersmooth Equivalence Relations." Thesis, University of North Texas, 2019. https://digital.library.unt.edu/ark:/67531/metadc1505289/.

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We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian groups.
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Iverson, Joseph. "Frames Generated by Actions of Locally Compact Groups." Thesis, University of Oregon, 2016. http://hdl.handle.net/1794/20443.

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Let $G$ be a second countable, locally compact group which is either compact or abelian, and let $\rho$ be a unitary representation of $G$ on a separable Hilbert space $\mathcal{H}_\rho$. We examine frames of the form $\{ \rho(x) f_j \colon x \in G, j \in I\}$ for families $\{f_j\}_{j \in I}$ in $\mathcal{H}_\rho$. In particular, we give necessary and sufficient conditions for the joint orbit of a family of vectors in $\mathcal{H}_\rho$ to form a continuous frame. We pay special attention to this problem in the setting of shift invariance. In other words, we fix a larger second countable loc
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Whitfield, John Brian. "On the spectrum G of a locally compact group G." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0024/MQ52086.pdf.

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Norling, Magnus Dahler. "Topological Dynamics and Algebra in the Spectrum of L infinity of a locally compact Group : With Application to Crossed Products." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9889.

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<p>In this text, I will look at some new approaches that may shed some light on the Kadison Singer problem, mainly one instigated by Vern Paulsen using dynamical systems in the Stone-Cech compactification of a discrete group. In order to do this, I will try to develop the theory in a crossed product setting, and look at some aspects of it that may hold interest of their own.</p>
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Solomyak, Margarita. "Essential spanning forests and electric networks in groups /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5767.

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LO, YU-CHING, and 羅郁卿. "M1 Algebra on Some Totally Disconnected,Locally Compact Abelian Group." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/35473896120111921861.

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博士<br>國立中央大學<br>數學系<br>84<br>In this paper we intend to investigated M1 space, and to genera- lize M1 space on totally disconnected, second countable, locally compact abelian group G. In section one, we prove that M1(G) is a Banach algebra and L1-Banach module, and M1(G) is a subspace of the intersection of L1(G) and C0(G). In section two, we construct a example which is belonged to M1 space but not to L1 space.In section three, we prove a result concerning the dual space M1*(G) to M1(G). I
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Safoura, Zaffar Jafar Zadeh. "Isomorphisms of Banach algebras associated with locally compact groups." 2015. http://hdl.handle.net/1993/30932.

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The main theme of this thesis is to study the isometric algebra isomorphisms and the bipositive algebra isomorphisms between various Banach algebras associated with locally compact groups. Let $LUC(G)$ denote the $C^*$-algebra of left uniformly continuous functions with the uniform norm and let $C_0(G)^{\perp}$ denote the annihilator of $C_0(G)$ in $LUC(G)^*$. In Chapter 2 of this thesis, among other results, we show that if $G$ is a locally compact group and $H$ is a discrete group then whenever there exists a weak-star continuous isometric isomorphism between $C_0(G)^{\perp}$ and $C_0(H)^
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Books on the topic "Locally compact abelian group"

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Osipov, V. F. Analiz Bora-Furʹe na lokalʹno kompaktnykh kommutativnykh gruppakh: Uchebnoe posobie. Leningradskiĭ gos. universitet im. A.A. Zhdanova, 1988.

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Reiter, Hans. Metaplectic groups and Segal algebras. Springer-Verlag, 1989.

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Cornulier, Yves. Metric geometry of locally compact groups. European Mathematical Society, 2016.

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S, Doran Robert, ed. Representations of [asterix]-algebras, locally compact groups, and Banach [asterix]-algebraic bundles. Academic Press, 1988.

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J, Sally Paul. Fundamentals of mathematical analysis. American Mathematical Society, 2013.

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I, Li͡ubich I͡U. Introduction to the theory of Banach representations of groups. Birkhäuser Verlag, 1988.

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Simon, Barry. Operator theory. American Mathematical Society, 2015.

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Tao, Terence. Hilbert's fifth problem and related topics. American Mathematical Society, 2014.

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1938-, Griffiths Phillip, and Kerr Matthew D. 1975-, eds. Hodge theory, complex geometry, and representation theory. Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2013.

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Koli︠a︡da, S. F. Dynamics and numbers: A special program, June 1-July 31, 2014, Max Planck Institute for Mathematics, Bonn, Germany : international conference, July 21-25, 2014, Max Planck Institute for Mathematics, Bonn, Germany. Edited by Max-Planck-Institut für Mathematik. American Mathematical Society, 2016.

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Book chapters on the topic "Locally compact abelian group"

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Bishop, Errett, and Douglas Bridges. "Locally Compact Abelian Groups." In Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-61667-9_9.

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Ramakrishnan, Dinakar, and Robert J. Valenza. "Duality for Locally Compact Abelian Groups." In Graduate Texts in Mathematics. Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4757-3085-2_3.

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Christensen, Ole. "Frames on Locally Compact Abelian Groups." In Applied and Numerical Harmonic Analysis. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-25613-9_21.

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Lyubich, Yurii I. "Representations of Locally Compact Abelian Groups." In Introduction to the Theory of Banach Representations of Groups. Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9169-1_5.

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Kodaira, Kunihiko. "( 11 ) Normed ring of a locally compact abelian group." In Kunihiko Kodaira: Collected Works, Volume I. Princeton University Press, 2015. http://dx.doi.org/10.1515/9781400869855-012.

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Koch, Helmut. "Harmonic analysis on locally compact abelian groups." In Graduate Studies in Mathematics. American Mathematical Society, 2000. http://dx.doi.org/10.1090/gsm/024/13.

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Terauds, Venta. "Doubly Sparse Measures on Locally Compact Abelian Groups." In 2019-20 MATRIX Annals. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-62497-2_56.

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Gröchenig, Karlheinz. "Aspects of Gabor analysis on locally compact abelian groups." In Gabor Analysis and Algorithms. Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4612-2016-9_7.

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Schlottmann, Martin. "Cut-and-project sets in locally compact Abelian groups." In Quasicrystals and Discrete Geometry. American Mathematical Society, 1998. http://dx.doi.org/10.1090/fim/010/09.

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Esquível, Manuel L., and Nadezhda P. Krasii. "Random Tempered Distributions on Locally Compact Separable Abelian Groups." In Operator Theory and Harmonic Analysis. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76829-4_7.

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Conference papers on the topic "Locally compact abelian group"

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King, Emily J. "Frame theory for locally compact abelian groups." In SPIE Optical Engineering + Applications, edited by Dimitri Van De Ville, Vivek K. Goyal, and Manos Papadakis. SPIE, 2013. http://dx.doi.org/10.1117/12.2025018.

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HEYER, HERBERT, and GYULA PAP. "On infinite divisibility and embedding of probability measures on a locally compact Abelian group." In Proceedings of the Third German-Japanese Symposium. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701503_0007.

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PANDEY, S. S. "GABOR MULTIPLIERS FOR BANACH SPACES OF DISTRIBUTIONS ON LOCALLY COMPACT ABELIAN GROUPS." In Proceedings of the International Computer Conference 2006. World Scientific Publishing Company, 2006. http://dx.doi.org/10.1142/9789812772763_0001.

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Reports on the topic "Locally compact abelian group"

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Gadella, Manuel, and Fernando Go'mez. Riggings of Locally Compact Abelian Groups. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-11-2008-23-31.

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Berner, Chad. Shift-invariant subspaces of locally compact abelian groups. Iowa State University, 2021. http://dx.doi.org/10.31274/cc-20240624-1284.

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