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Graduate Texts in Mathematics #192: Elements of Functional Analysisby Francis Hirsch
Synopses & Reviews
This is a graduate text on functional analysis. After presenting the fundamental function spaces and their duals, the authors study topics in operator theory and finally develop the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems.Along the way, the reader is presented with a truly remarkable assortment of well formulated and interesting exercises, which test the understanding as well as point out many related topics. The answers and hints that are not already contained in the statements of the exercises are collected at the end of the book.
The authors' goal in this book on functional analysis is to introduce the reader to the theory of distributions, differential operators, and Sobolev spaces. Along the way, the reader is presented.with a truly remarkable assortment of well formulated interesting and solved exercises which test the understanding as well as point out many related topics.
This book presents the fundamental function spaces and their duals, explores operator theory and finally develops the theory of distributions up to significant applications such as Sobolev spaces and Dirichlet problems. Includes an assortment of well formulated exercises, with answers and hints collected at the end of the book.
Includes bibliographical references (p. -386) and index.
Table of Contents
I. Function Spaces and Their Duals: The Space of Continous Functions on a Compact Set.- Locally Compact Spaces and Radon Measures.- Hilbert Spaces.- Lp Spaces; II. Operators: Spectra.- Compact Operators; III. Distributions: Definitions and Examples.- Multiplication and Differentiation.- Convolution of Distributions.- The Laplacian on an Open Set.
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