Essential Results of Functional Analysis (Chicago Lectures in Mathematics) 1st Edition by Robert J. Zimmer (PDF)

Description

Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach. Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer’s emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter. For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.

User’s Reviews

Editorial Reviews: From the Back Cover Chicago Lectures in Mathematics Essential results in Mathematics series . Includes a Bibliographical reference.This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. About the Author Robert J. Zimmer is professor of mathematics at the University of Chicago. He is the author of Ergodic Theory and Semisimple Groups.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Creo que este es una de las revisiones mas completas sobre Analisis Funcional que he podido leer , creo da un espectro completo de el Analisis Funcional, el modo en que se encara cada capitulo tiene un estilo muy particular, en especial los ejemplos son tan ilustrativos que forman parte esencial del libro, considero este un trabajo realmente bueno, como pocos en esta tan fructifera area…

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