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Дисертації з теми "Compact groups"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 29 липня 2024

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1

Chung, Kin Hoong School of Mathematics UNSW. "Compact Group Actions and Harmonic Analysis." Awarded by:University of New South Wales. School of Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17639.

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A large part of the structure of the objects in the theory of Dooley and Wildberger [Funktsional. Anal. I Prilozhen. 27 (1993), no. 1, 25-32] and that of Rouviere [Compositio Math. 73 (1990), no. 3, 241-270] can be described by considering a connected, finite-dimentional symmetric space G/H (as defined by Rouviere), with ???exponential map???, Exp, from L G/L H to G/H, an action, ???: K ??? Aut??(G) (where Aut?? (G) is the projection onto G/H of all the automorphisms of G which leave H invariant), of a Lie group, K, on G/H and the corresponding action, ???# , of K on L G/L H defined by g ??? L

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2

Pittau, Lorenzo. "Le produit en couronne libre d'un groupe quantique compact par un groupe quantique d'automorphismes." Thesis, Cergy-Pontoise, 2015. http://www.theses.fr/2015CERG0781/document.

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Dans cette thèse on définit et étudie le produit en couronne libre d'un groupe quantique compact par un groupe quantique d'automorphismes, en généralisant la notion de produit en couronne libre par le groupe quantique symétrique introduit par Bichon.Notre recherche est divisée en deux parties. Dans la première, on définit le produit en couronne libre d'un groupe discret par un groupe quantique d'automorphismes. Ensuite, on montre comment décrire les entrelaceurs de ce nouveau objet à l'aide de partitions non-croisées et décorées; à partir de cela et grâce à un résultat de Lemeux, on déduise le

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3

Bauer, Tilman 1973. "[rho]-compact groups as framed manifolds." Thesis, Massachusetts Institute of Technology, 2002. http://hdl.handle.net/1721.1/8401.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.<br>In title on t.p. "[rho]" appears as the lower-case Greek letter.<br>Includes bibliographical references (p. 57-59).<br>We describe a natural way to associate to any [rho]-compact group an element of the [rho]-local stable stems, which, applied to the [rho]-completion of a compact Lie group G, coincides with the element represented by the manifold G with its left-invariant framing. To this end, we construct a d-dimensional sphere SG with a stable G-action for every d-dimensional [rho]-compact group G, which g

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4

Elkasapy, Abdelrhman. "Word Maps on Compact Lie Groups." Doctoral thesis, Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-184066.

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5

Stolz, Abel. "Linear Approximation of Groups and Ultraproducts of Compact Simple Groups." Doctoral thesis, Universitätsbibliothek Leipzig, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-125643.

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Анотація:

We derive basic properties of groups which can be approximated with matrices. These include closure of classes of such groups under group theoretic constructions including direct and inverse limits and free products. We show that metric ultraproducts of projective linear groups over fields of different characteristics are not isomorphic. We further prove that the lattice of normal subgroups in ultraproducts of compact simple groups is distributive. It is linearly ordered in the case of finite simple groups or Lie groups of bounded rank.

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6

Metelichenko, Oleksandr Borisovich. "The isodiametric inequality in locally compact groups." Thesis, University College London (University of London), 2006. http://discovery.ucl.ac.uk/1444835/.

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In this thesis it is shown that the isodiametric inequality fails for Carnot-Caratheodory balls in the Heisenberg group W (n E N). Estimates for the ratio of the volume of a ball to the maximal volume of a set of the same diameter are established in this group, and the set of the maximal volume is also found among all sets of revolution about the vertical axis having the same diameter. Results of the similar nature are obtained in the additive group Rn+1 (n G N) with non-isotropic dilations. Using a connection between the isodiametric problem and the Besicovitch 1/2-problem it is proved that t

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7

Trotter, Steven. "Involutive algebras and locally compact quantum groups." Thesis, University of Leeds, 2016. http://etheses.whiterose.ac.uk/16168/.

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In this thesis we will be concerned with some questions regarding involutions on dual and predual spaces of certain algebras arising from locally compact quantum groups. In particular we have the $L^1(\G)$ predual of a von Neumann algebraic quantum group $(L^\infty(\G), \Delta)$. This is a Banach algebra (where the product is given by the pre-adjoint of the coproduct $\Delta$), however in general we cannot make this into a Banach $*$-algebra in such a way that the regular representation is a $*$-homomorphism. We can however find a dense $*$-subalgebra $L^1_\sharp(\G)$ that satisfies this prope

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8

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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9

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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10

Junod, Fabien. "Unstable Adams operations on ρ-local compact groups". Thesis, University of Aberdeen, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.531931.

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Анотація:

Let <i>G</i> be any compact connected Lie group and let <i>T</i> ≤ <i>G</i> be a maximal torus. Then for any unstable Adams operation <i>f</i> of degree <i>k</i>, the following diagram commutes up to homotopy «!» And conversely, any map <i>f</i> that makes the above diagram commute must be an unstable Adams operation. Using this characterization, we will construct a self-map of a <i>p</i>-local compact group (<i>S,F,L</i>) in order to define unstable Adams operations on a more general setting. THEOREM. For any <i>p</i>-local compact group (<i>S,F,L</i>) there is a self-equivalence such that

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11

Yasemin, Talu E. "p-groups of automorphisms of compact Riemann surfaces." Thesis, University of Aberdeen, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357987.

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12

McGuire, Alex Bernard. "Partially ordered Abelian groups and linearly compact domains." Thesis, University of Essex, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.359787.

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13

Akylzhanov, Rauan. "Lp-Lq Fourier multipliers on locally compact groups." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/60829.

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We study the Lp − Lq boundedness of both spectral and Fourier multi- pliers on general locally compact separable unimodular groups G. As a consequence of the established Fourier multiplier theorem we also derive a spectral multiplier theorem on general locally compact separable uni- modular groups. We then apply it to obtain embedding theorems as well as time-asymptotics for the Lp − Lq norms of the heat kernels for general positive unbounded invariant operators on G. We illustrate the obtained results for sub-Laplacians on compact Lie groups and on the Heisenberg group, as well as for higher

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14

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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15

Rumbelow, Sam. "Pseudodifferential operators on compact abelian groups with applications." Thesis, Swansea University, 2006. https://cronfa.swan.ac.uk/Record/cronfa42386.

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Pseudodifferential operators on compact groups are discussed, with an emphasis on the conditions for which the theorem of Hille and Yosida holds. Some preliminary functional analysis is given including the notion of regularly dissipative operators and Pontrjagin duality. The dual group is described, especially that it is discrete. Some important inequalities, such as Young's inequality, are also stated. Generalised trigonometrical polynomials and generalised Sobolev spaces are defined on the compact group G. A finite exhaustion of the dual space is used to define pointwise convergence and to g

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16

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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17

Cohen, Michael Patrick. "Descriptive Set Theory and Measure Theory in Locally Compact and Non-locally Compact Groups." Thesis, University of North Texas, 2013. https://digital.library.unt.edu/ark:/67531/metadc271792/.

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In this thesis we study descriptive-set-theoretic and measure-theoretic properties of Polish groups, with a thematic emphasis on the contrast between groups which are locally compact and those which are not. The work is divided into three major sections. In the first, working jointly with Robert Kallman, we resolve a conjecture of Gleason regarding the Polish topologization of abstract groups of homeomorphisms. We show that Gleason's conjecture is false, and its conclusion is only true when the hypotheses are considerably strengthened. Along the way we discover a new automatic continuity resul

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18

Vergara, Soto Ignacio. "Multipliers and approximation properties of groups." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEN042/document.

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Cette thèse porte sur des propriétés d'approximation généralisant la moyennabilité pour les groupes localement compacts. Ces propriétés sont définies à partir des multiplicateurs de certaines algèbres associés aux groupes. La première partie est consacrée à l'étude de la propriété p-AP, qui est une extension de la AP de Haagerup et Kraus au cadre des opérateurs sur les espaces Lp. Le résultat principal dit que les groupes de Lie simples de rang supérieur et de centre fini ne satisfont p-AP pour aucun p entre 1 et l'infini. La deuxième partie se concentre sur les multiplicateurs de Schur radiau

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19

Ghatei, Davoud. "Spin covers of maximal compact subgroups of Kac-Moody groups and of Weyl groups." Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/6027/.

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The maximal compact subgroup SO(\(n\),ℝ) of SL(\(n\),ℝ) admits two double covers Spin (\(n\),ℝ) and O(\(n\),ℝ). In this thesis we show that in fact given any simply-laced diagram ∆, with associated split real Kac-Moody group \(G\)(∆), the 'maximal compact' subgroup \(K\)(∆)also admits a double cover Spin(∆). We then describe a subgroup of Spin(∆) which is a cover of the Weyl group \(W\)(∆) associated to g(∆). This answers a conjecture of Damour and Hillmann. Moreover, the group \(D\) which extends \(W\) is used in an attempt to classify the images of the so-called generalised spin representati

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20

Watson, Paul Daniel. "Symmetries and automorphisms of compact Riemann surfaces." Thesis, University of Southampton, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294489.

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21

Le, Boudec Adrien. "Géométrie des groupes localement compacts. Arbres. Action !" Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112036.

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Dans le Chapitre 1 nous étudions les groupes localement compacts lacunaires hyperboliques. Nous caractérisons les groupes ayant un cône asymptotique qui est un arbre réel et dont l'action naturelle est focale. Nous étudions également la structure des groupes lacunaires hyperboliques, et montrons que dans le cas unimodulaire les sous-groupes ne satisfont pas de loi. Nous appliquons au Chapitre 2 les résultats précédents pour résoudre le problème de l'existence de points de coupure dans un cône asymptotique dans le cas des groupes de Lie connexes. Dans le Chapitre 3 nous montrons que le groupe d

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22

Lozano, Bagén Toni. "On the exoticness of some new p-local compact groups." Doctoral thesis, Universitat Autònoma de Barcelona, 2016. http://hdl.handle.net/10803/385105.

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En 2003, Broto-Levi-Oliver van introduir el concepte de grup p-local finit, el qual és una generalització dels espais classificadors de grups finits p-completats. Més tard, els mateixos autors van introduir també el concepte de grup p-local compacte, el qual és una generalització dels espais classificadors de grups de Lie p-completats i dels grups p-compactes. Mentre que el concepte de grup p-local finit exòtic està clarament definit, en el cas compacte hi ha vàries famílies de grups que donen lloc a grups p-locals compactes, desdibuixant així la noció d'exoticitat. En aquesta tesi construi

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23

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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24

Bär, Christian. "Elliptische Operatoren und Darstellungstheorie kompakter Gruppen." Bonn : [s.n.], 1993. http://catalog.hathitrust.org/api/volumes/oclc/31453453.html.

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25

Krusch, Elvira. "Investigation of the dwarf galaxy population in Hickson compact groups." [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=970841698.

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26

Johnstone, Stephen. "Theory and applications of Fourier multipliers on locally compact groups." Thesis, University of Strathclyde, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.443141.

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27

Evens, Samuel R. (Samuel Robert). "Transfer for compact lie groups, induced representations, and braid relations." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/80453.

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28

Gül, Erdal. "Controllability of linear systems on non-abelian compact lie groups." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96429.

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In this paper, we shall deal with a linear control system ∑ defined on a Lie group G with Lie algebra L(G). We prove that, if G is a compact connected Lie group, then the vector fields associated to dynamic of ∑ are conservative, and that if G is also non-Abelian then, by using Poincare Theorem, ∑ is transitive if and only if it is controllable.

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29

Cave, Christopher. "On coarse geometric properties of discrete and locally compact groups." Thesis, University of Southampton, 2015. https://eprints.soton.ac.uk/384182/.

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30

Biller, Harald. "Actions of compact groups on spheres and on generalized quadrangles." [S.l. : s.n.], 1999. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB8189670.

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31

Yu, Jun. "Symmetric subgroups of automorphism groups of compact simple Lie algebras /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?MATH%202009%20YU.

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32

Gromada, Daniel [Verfasser]. "Compact matrix quantum groups and their representation categories / Daniel Gromada." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2020. http://d-nb.info/1219068810/34.

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33

Mamino, Marcello. "Topological results on definably compact groups in o-minimal structures." Doctoral thesis, Scuola Normale Superiore, 2010. http://hdl.handle.net/11384/85665.

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34

Walter, Boris [Verfasser]. "Weighted diffeomorphism groups of Banach spaces and non-compact manifolds and weighted mapping groups / Boris Walter." Paderborn : Universitätsbibliothek, 2014. http://d-nb.info/1058165399/34.

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35

Crespo, Jonathan. "Monoidal equivalence of locally compact quantum groups and application to bivariant K-theory." Thesis, Clermont-Ferrand 2, 2015. http://www.theses.fr/2015CLF22621/document.

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Les travaux présentés dans cette thèse concernent l'équivalence monoïdale de groupes quantiques localement compacts et ses applications. Nous généralisons au cas localement compact et régulier, deux résultats importants concernant les actions de groupes quantiques compacts. Soient G1 et G2 deux groupes quantiques localement compacts réguliers et monoïdalement équivalents. Nous développons un procédé d'induction des actions qui permet d'établir une équivalence canonique des catégories dont les objets sont les actions continues de G1 et G2 sur les C*-algèbres. Comme application de ce résultat, n

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36

Renedo, Marco Antonio. "Mixing properties of actions by commuting epimorphisms of Compact Abelian Groups /." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487953567771096.

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37

Kazeem, Funmilayo Eniola. "A measure for the number of commuting subgroups in compact groups." Doctoral thesis, Faculty of Science, 2019. http://hdl.handle.net/11427/30383.

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The present thesis is devoted to the construction of a probability measure which counts the pairs of closed commuting subgroups in infinite groups. This measure turns out to be an extension of what was known in the finite case as subgroup commutativity degree and opens a new approach of study for the class of near abelian groups, recently introduced in [24, 27]. The extremal case of probability one characterises the topologically quasihamiltonian groups, studied originally by K. Iwasawa [30, 31] in the abstract case and then by F. K¨ummich [35, 36, 37], C. Scheiderer [45, 46], P. Diaconis [11]

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38

Maher, David Graham School of Mathematics UNSW. "Brownian motion and heat kernels on compact lie groups and symmetric spaces." Awarded by:University of New South Wales. School of Mathematics, 2006. http://handle.unsw.edu.au/1959.4/28295.

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An important object of study in harmonic analysis is the heat equation. On a Euclidean space, the fundamental solution of the associated semigroup is known as the heat kernel, which is also the law of Brownian motion. Similar statements also hold in the case of a Lie group. By using the wrapping map of Dooley and ildberger, we show how to wrap a Brownian motion to a compact Lie group from its Lie algebra (viewed as a Euclidean space) and find the heat kernel. This is achieved by considering It??o type stochastic differential equations and applying the Feynman-Ka??c theorem. We also consider wr

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39

O'Brien, Ellen Marie. "Finitely asymptotic properties of powers of characters of compact semisimple Lie groups." Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/10307.

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This thesis has to do with decomposing tensor powers of irreducible representations of compact semisimple Lie groups or their Lie algebras. We will be concerned only with the set of irreducible representations appearing in the decomposition. In particular, we determine whether, for a sufficiently high tensor power, this set is "maximal", in a sense to be made more precise below. We rely on the theory of semisimple Lie algebras, and describe the results in terms of characters. A (reducible) character of a finite dimensional complex semisimple Lie algebra is saturated if for each of its dominant

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40

Vassar, Susan. "A study of compact groups selected from the APM Bright Galaxy Catalogue." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260177.

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41

馮淑貞 and Suk-ching Fung. "Asymptotic vanishing theorem of cohomology groups on compact quotientsof the unit ball." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31220848.

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42

Deutsch, Annabel. "Kazhdan's property (T) and related properties of locally compact and discrete groups." Thesis, University of Edinburgh, 1992. http://hdl.handle.net/1842/13631.

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In this thesis we look at a number of properties related to Kazhdan's property (T), for a locally compact, metrisable, σ-compact group. For such a group, <i>G</i>, the following properties are equivalent. 1. Kazhdan's definition of property (T): the trivial representations is isolated in the unitary dual of <i>G</i> (with the Fell topology). 2. The group, <i>G</i>, is compactly generated and for every compact generating set, <i>K</i>, there is a positive constant, ε, such that if π is a unitary representation of <i>G</i> on a Hilbert space, cal H, and ζ is a unit vector in cal H such that vski

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43

Miles, Richard Craig. "Arithmetic dynamical systems." Thesis, University of East Anglia, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323222.

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44

Wang, Xumin. "Functional and harmonic analysis of noncommutative Lp spaces associated to compact quantum groups." Thesis, Bourgogne Franche-Comté, 2019. http://www.theses.fr/2019UBFCD040.

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Cette thèse a pour but d'étudier l'analyse sur les groupes quantiques compacts. Elle se compose de deux parties. La première présente la classification des semi-groupes de Markov invariants sur ces espaces homogènes quantiques. Les générateurs de ces semi-groupes sont considérés comme des opérateurs de Laplace sur ces espaces.La sphère classique , la sphère libre et la sphère semi-libérée sont considérées comme des exemples et les générateurs de semi-groupes de Markov sur ces sphères sont classés. Nous calculons aussi les dimensions spectrales des trois familles de sphères en fonction du compo

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45

Kindl, Enrico. "A photometric and morphological study of compact groups of galaxies and their environments." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/30722.

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This thesis examines properties of galaxies in and around compact groups. Astrometry, photometry and morphological classifications are derived from CCD images for all 463 galaxies in Hickson's sample of 100 compact groups. Some minor revisions to the membership of the original catalog are made. At high galactic latitude (b > 30°), the catalog is estimated to be 90% complete for groups with total B[formula omitted] magnitude 13.0 or less. 49% of all the catalogued galaxies, and 48% of first-ranked galaxies are spiral. No significant difference is found between the distribution of morphological

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46

Kliemann, Malte [Verfasser]. "The Thickness of Left-Invariant Metrics on Compact Connected Lie Groups / Malte Kliemann." Kiel : Universitätsbibliothek Kiel, 2019. http://d-nb.info/1177797887/34.

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47

Schneider, Jakob [Verfasser], Andreas [Gutachter] Thom, and Martin [Gutachter] Liebeck. "On ultraproducts of compact quasisimple groups / Jakob Schneider ; Gutachter: Andreas Thom, Martin Liebeck." Dresden : Technische Universität Dresden, 2021. http://d-nb.info/1232413577/34.

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48

Fung, Suk-ching. "Asymptotic vanishing theorem of cohomology groups on compact quotients of the unit ball /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B20667991.

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49

Bywaters, Timothy Peter. "Connections Between Willis' Theory for Totally Disconnected Locally Compact Groups and Graph Automorphisms." Thesis, The University of Sydney, 2019. http://hdl.handle.net/2123/21148.

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We investigate the tidy subgroups, scale function and related invariants of totally disconnected locally compact groups. Our focus is on relating these ideas to combinatorial and geometric aspects of the group. After giving necessary background, we study the scale function and tidy subgroups of an endomorphism of a totally disconnected locally compact group. Our results are inspired by a similar investigation for automorphisms by Möller (Can. J. Math., 54(4), 795-827). We characterise when a compact open subgroup is tidy for an endomorphism in terms of a graph constructed from the subgroups a

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50

Stolz, Abel [Verfasser], Andreas [Akademischer Betreuer] Thom, Andreas [Gutachter] Thom, and Nikolay [Gutachter] Nikolov. "Linear Approximation of Groups and Ultraproducts of Compact Simple Groups / Abel Stolz ; Gutachter: Andreas Thom, Nikolay Nikolov ; Betreuer: Andreas Thom." Leipzig : Universitätsbibliothek Leipzig, 2013. http://d-nb.info/1238527353/34.

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