Topological Groups and the Pontryagin-van Kampen Duality

Topological Groups and the Pontryagin-van Kampen Duality
Author: Lydia Außenhofer
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 392
Release: 2021-11-22
Genre: Mathematics
ISBN: 3110654938

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.

Topological Groups

Topological Groups
Author: Dikran Dikranjan
Publisher:
Total Pages: 412
Release: 2021-11-24
Genre:
ISBN: 9783110653496

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 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) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020) 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)

Pontryagin Duality and the Structure of Locally Compact Abelian Groups

Pontryagin Duality and the Structure of Locally Compact Abelian Groups
Author: Sidney A. Morris
Publisher: Cambridge University Press
Total Pages: 141
Release: 1977-08-04
Genre: Mathematics
ISBN: 0521215439

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.

Introduction to Topological Groups

Introduction to Topological Groups
Author: Taqdir Husain
Publisher: Courier Dover Publications
Total Pages: 241
Release: 2018-02-15
Genre: Mathematics
ISBN: 0486819191

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.

Topological Groups and Related Structures, An Introduction to Topological Algebra.

Topological Groups and Related Structures, An Introduction to Topological Algebra.
Author: Alexander Arhangel’skii
Publisher: Springer Science & Business Media
Total Pages: 794
Release: 2008-05-01
Genre: Mathematics
ISBN: 949121635X

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.

Pontryagin Duality and the Structure of Locally Compact Abelian Groups

Pontryagin Duality and the Structure of Locally Compact Abelian Groups
Author: Sidney A. Morris
Publisher:
Total Pages: 138
Release: 2014-05-14
Genre: MATHEMATICS
ISBN: 9781107360877

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.

Functional Analysis and Continuous Optimization

Functional Analysis and Continuous Optimization
Author: José M. Amigó
Publisher: Springer Nature
Total Pages: 273
Release: 2023-07-01
Genre: Mathematics
ISBN: 3031300149

The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.

Stereotype Spaces and Algebras

Stereotype Spaces and Algebras
Author: Sergei S. Akbarov
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 871
Release: 2022-08-22
Genre: Mathematics
ISBN: 3110780968

The term “stereotype space” was introduced in 1995 and denotes a category of locally convex spaces with surprisingly elegant properties. Its study gives an unexpected point of view on functional analysis that brings this fi eld closer to other main branches of mathematics, namely, to algebra and geometry. This volume contains the foundations of the theory of stereotype spaces, with accurate definitions, formulations, proofs, and numerous examples illustrating the interaction of this discipline with the category theory, the theory of Hopf algebras, and the four big geometric disciplines: topology, differential geometry, complex geometry, and algebraic geometry.

Hopf Algebras, Quantum Groups and Yang-Baxter Equations

Hopf Algebras, Quantum Groups and Yang-Baxter Equations
Author: Florin Felix Nichita
Publisher: MDPI
Total Pages: 239
Release: 2019-01-31
Genre: Mathematics
ISBN: 3038973246

This book is a printed edition of the Special Issue "Hopf Algebras, Quantum Groups and Yang-Baxter Equations" that was published in Axioms