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.
Review
"This book is an advanced textbook on functional analysis with an emphasis on spaces of classical and generalized functions (the book arose from a course taught for several years at the University of Evry-Val d'Essone). The basic merits of this interesting book are an elementary and transparent account of basic notations, constructions, and results of functional analysis, and a brilliant and rich set (more than 400) of well-formulated and interesting exercises. The latter not only essentially enlarge the basic contents of the book, but are a good school in functional analysis under the condition of their consecutive solving in this book one can find other remarkable results of functional analysis, which are presented with skilful pedagogical mastery. Undoubtedly, the book will be useful for researchers and lectures of functional analysis or special courses in the field as well as for students of different level which study or want to study functional analysis and its applications. ZENTRALBLATT MATH"
Synopsis
This book arose from a course taught for several years at the Univer sity of Evry-Val d'Essonne. It is meant primarily for graduate students in mathematics. To make it into a useful tool, appropriate to their knowl edge level, prerequisites have been reduced to a minimum: essentially, basic concepts of topology of metric spaces and in particular of normed spaces (convergence of sequences, continuity, compactness, completeness), of "ab stract" integration theory with respect to a measure (especially Lebesgue measure), and of differential calculus in several variables. The book may also help more advanced students and researchers perfect their knowledge of certain topics. The index and the relative independence of the chapters should make this type of usage easy. The important role played by exercises is one of the distinguishing fea tures of this work. The exercises are very numerous and written in detail, with hints that should allow the reader to overcome any difficulty. Answers that do not appear in the statements are collected at the end of the volume. There are also many simple application exercises to test the reader's understanding of the text, and exercises containing examples and coun terexamples, applications of the main results from the text, or digressions to introduce new concepts and present important applications. Thus the text and the exercises are intimately connected and complement each other."
Synopsis
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.
Synopsis
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.
Description
Includes bibliographical references (p. [385]-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.