Advanced Real Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advanced Real Analysis write by Anthony W. Knapp. This book was released on 2008-07-11. Advanced Real Analysis available in PDF, EPUB and Kindle. * Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Locally Compact Groups
Locally Compact Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Locally Compact Groups write by Markus Stroppel. This book was released on 2006. Locally Compact Groups available in PDF, EPUB and Kindle. 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.
Metric Geometry of Locally Compact Groups
Metric Geometry of Locally Compact Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Metric Geometry of Locally Compact Groups write by Yves Cornulier. This book was released on 2016. Metric Geometry of Locally Compact Groups available in PDF, EPUB and Kindle. 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.
New Directions in Locally Compact Groups
New Directions in Locally Compact Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Directions in Locally Compact Groups write by Pierre-Emmanuel Caprace. This book was released on 2018-02-08. New Directions in Locally Compact Groups available in PDF, EPUB and Kindle. A snapshot of the major renaissance happening today in the study of locally compact groups and their many applications.
Introduction to the Representation Theory of Compact and Locally Compact Groups
Introduction to the Representation Theory of Compact and Locally Compact Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to the Representation Theory of Compact and Locally Compact Groups write by Alain Robert. This book was released on 1983-02-10. Introduction to the Representation Theory of Compact and Locally Compact Groups available in PDF, EPUB and Kindle. Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.
