The Structure Of Locally Compact Abelian Groups

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Pontryagin Duality And The Structure Of Locally Compact Abelian Groups

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Author : Sidney A. Morris
language : en
Publisher: Cambridge University Press
Release Date : 1977-08-04

Pontryagin Duality And The Structure Of Locally Compact Abelian Groups written by Sidney A. Morris and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-08-04 with Mathematics categories.

These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.

The Structure Of Locally Compact Abelian Groups

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Author : David L. Armacost
language : en
Publisher:
Release Date : 1981

The Structure Of Locally Compact Abelian Groups written by David L. Armacost and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

Fourier Analysis On Groups

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Author : Walter Rudin
language : en
Publisher: Courier Dover Publications
Release Date : 2017-04-19

Fourier Analysis On Groups written by Walter Rudin and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-19 with Mathematics categories.

Self-contained treatment by a master mathematical expositor ranges from introductory chapters on basic theorems of Fourier analysis and structure of locally compact Abelian groups to extensive appendixes on topology, topological groups, more. 1962 edition.

Introduction To Topological Groups

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Author : Taqdir Husain
language : en
Publisher: Courier Dover Publications
Release Date : 2018-02-15

Introduction To Topological Groups written by Taqdir Husain and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-15 with Mathematics categories.

Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.

Periodic Locally Compact Groups

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Author : Wolfgang Herfort
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-19

Periodic Locally Compact Groups written by Wolfgang Herfort and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-19 with Mathematics categories.

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

Topological Groups And Related Structures An Introduction To Topological Algebra

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Author : Alexander Arhangel’skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-01

Topological Groups And Related Structures An Introduction To Topological Algebra written by Alexander Arhangel’skii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-01 with Mathematics categories.

Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.

Lecture Notes On The Structure Of Locally Compact Abelian Groups And The Pontryagin Van Kampen Duality Theorem

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Author : Sidney A. Morris
language : en
Publisher:
Release Date : 1974

Lecture Notes On The Structure Of Locally Compact Abelian Groups And The Pontryagin Van Kampen Duality Theorem written by Sidney A. Morris and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.

2019 20 Matrix Annals

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Author : Jan de Gier
language : en
Publisher: Springer Nature
Release Date : 2021-02-10

2019 20 Matrix Annals written by Jan de Gier and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.

MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Metric Geometry Of Locally Compact Groups

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Author : Yves Cornulier
language : en
Publisher: European Mathematical Society
Release Date : 2016

Metric Geometry Of Locally Compact Groups written by Yves Cornulier and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.

The main aim of this book is the study of locally compact groups from a geometric perspective, with an emphasis on appropriate metrics that can be defined on them. The approach has been successful for finitely generated groups and can be favorably extended to locally compact groups. Parts of the book address the coarse geometry of metric spaces, where ``coarse'' refers to that part of geometry concerning properties that can be formulated in terms of large distances only. This point of view is instrumental in studying locally compact groups. Basic results in the subject are exposed with complete proofs; others are stated with appropriate references. Most importantly, the development of the theory is illustrated by numerous examples, including matrix groups with entries in the the field of real or complex numbers, or other locally compact fields such as $p$-adic fields, isometry groups of various metric spaces, and last but not least, discrete groups themselves. The book is aimed at graduate students, advanced undergraduate students, and mathematicians seeking some introduction to coarse geometry and locally compact groups.