Download or read book Periodic Locally Compact Groups written by Wolfgang Herfort and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-19 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups. The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with number theory and graph theory and illustrating it by a large exhibit of examples. Finally, the third part uses this theory for a complete, enlarged and novel presentation of Mukhin’s pioneering work generalizing to locally compact groups Iwasawa’s early investigations of the lattice of subgroups of abstract groups. Contents Part I: Background information on locally compact groups Locally compact spaces and groups Periodic locally compact groups and their Sylow theory Abelian periodic groups Scalar automorphisms and the mastergraph Inductively monothetic groups Part II: Near abelian groups The definition of near abelian groups Important consequences of the definitions Trivial near abelian groups The class of near abelian groups The Sylow structure of periodic nontrivial near abelian groups and their prime graphs A list of examples Part III: Applications Classifying topologically quasihamiltonian groups Locally compact groups with a modular subgroup lattice Strongly topologically quasihamiltonian groups

Download or read book Locally Compact Groups written by Markus Stroppel and published by European Mathematical Society. This book was released on 2006 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Locally compact groups play an important role in many areas of mathematics as well as in physics. The class of locally compact groups admits a strong structure theory, which allows to reduce many problems to groups constructed in various ways from the additive group of real numbers, the classical linear groups and from finite groups. The book gives a systematic and detailed introduction to the highlights of that theory. In the beginning, a review of fundamental tools from topology and the elementary theory of topological groups and transformation groups is presented. Completions, Haar integral, applications to linear representations culminating in the Peter-Weyl Theorem are treated. Pontryagin duality for locally compact Abelian groups forms a central topic of the book. Applications are given, including results about the structure of locally compact Abelian groups, and a structure theory for locally compact rings leading to the classification of locally compact fields. Topological semigroups are discussed in a separate chapter, with special attention to their relations to groups. The last chapter reviews results related to Hilbert's Fifth Problem, with the focus on structural results for non-Abelian connected locally compact groups that can be derived using approximation by Lie groups. The book is self-contained and is addressed to advanced undergraduate or graduate students in mathematics or physics. It can be used for one-semester courses on topological groups, on locally compact Abelian groups, or on topological algebra. Suggestions on course design are given in the preface. Each chapter is accompanied by a set of exercises that have been tested in classes.

Download or read book Periodic Locally Compact Groups written by Wolfgang Herfort and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-19 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups. The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with number theory and graph theory and illustrating it by a large exhibit of examples. Finally, the third part uses this theory for a complete, enlarged and novel presentation of Mukhin’s pioneering work generalizing to locally compact groups Iwasawa’s early investigations of the lattice of subgroups of abstract groups. Contents Part I: Background information on locally compact groups Locally compact spaces and groups Periodic locally compact groups and their Sylow theory Abelian periodic groups Scalar automorphisms and the mastergraph Inductively monothetic groups Part II: Near abelian groups The definition of near abelian groups Important consequences of the definitions Trivial near abelian groups The class of near abelian groups The Sylow structure of periodic nontrivial near abelian groups and their prime graphs A list of examples Part III: Applications Classifying topologically quasihamiltonian groups Locally compact groups with a modular subgroup lattice Strongly topologically quasihamiltonian groups

Download or read book Probability Measures on Locally Compact Groups written by H. Heyer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.

Download or read book The Structure of Compact Groups written by Karl H. Hofmann and published by Walter de Gruyter. This book was released on 2013-08-29 with total page 948 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject matter of compact groups is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics. This book serves the dual purpose of providing a textbook on it for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups. After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups, on compact Lie groups, and on locally compact abelian groups. Separate appended chapters contain the material for courses on abelian groups and on category theory. However, the thrust of the book points in the direction of the structure theory of not necessarily finite dimensional, nor necessarily commutative, compact groups, unfettered by weight restrictions or dimensional bounds. In the process it utilizes infinite dimensional Lie algebras and the exponential function of arbitrary compact groups. The first edition of 1998 and the second edition of 2006 were well received by reviewers and have been frequently quoted in the areas of instruction and research. For the present new edition the text has been cleaned of typographical flaws and the content has been conceptually sharpened in some places and polished and improved in others. New material has been added to various sections taking into account the progress of research on compact groups both by the authors and other writers. Motivation was provided, among other things, by questions about the structure of compact groups put to the authors by readers through the years following the earlier editions. Accordingly, the authors wished to clarify some aspects of the book which they felt needed improvement. The list of references has increased as the authors included recent publications pertinent to the content of the book.

Download or read book The Structure of Compact Groups written by Karl H. Hofmann and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-06-08 with total page 1034 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups. This fourth edition was updated with the latest developments in the field.

Download or read book Multipliers on Locally Compact Groups written by K. R. Parthasarathy and published by Springer. This book was released on 2006-11-14 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Almost Periodic Functions and Locally Compact Groups written by Milan Joshi and published by . This book was released on 2016-11-22 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Compact Semitopological Semigroups and Weakly Almost Periodic Functions written by J. F. Berglund and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Gabor Analysis and Algorithms written by Hans G. Feichtinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75] . . . ) but it does not constitute what we now call a frame, leading to numerical insta bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is "reasonably" smooth and localized. One is thus led naturally to considering a higher time-frequency density.

Download or read book Amenable Locally Compact Groups written by Jean-Paul Pier and published by Wiley-Interscience. This book was released on 1984-09-20 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collects the most recent results scattered throughout the literature on the theory of amenable groups, presenting a detailed investigation of the major features. The first part of the book discusses the different types of amenability properties, with basic examples listed. The second part provides complementary information on various aspects of amenability and a look at future directions.

Download or read book Representations of Locally Compact Groups with Applications written by T. H. Koornwinder and published by . This book was released on 1979 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book New Directions in Locally Compact Groups written by Pierre-Emmanuel Caprace and published by Cambridge University Press. This book was released on 2018-02-08 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.

Download or read book The Structure of Compact Groups written by Karl Heinrich Hofmann and published by Walter de Gruyter. This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Wolfgang Herfort, Karl H. Hofmann, and Francesco G. Russo, Periodic Locally Compact Groups: A Study of a Class of Totally Disconnected Topological Groups (2018) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antic, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)

Download or read book The Eberlein Compactification of Locally Compact Groups written by Elcim Elgun and published by . This book was released on 2012 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compact semigroup is, roughly, a semigroup compactification of a locally compact group if it contains a dense homomorphic image of the group. The theory of semigroup compactifications has been developed in connection with subalgebras of continuous bounded functions on locally compact groups. The Eberlein algebra of a locally compact group is defined to be the uniform closure of its Fourier-Stieltjes algebra. In this thesis, we study the semigroup compactification associated with the Eberlein algebra. It is called the Eberlein compactification and it can be constructed as the spectrum of the Eberlein algebra.

Download or read book Topological Groups and the Pontryagin van Kampen Duality written by Lydia Außenhofer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.

Download or read book Unitary Representations of Locally Compact Groups written by Louis Auslander and published by . This book was released on 1962 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: