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Free delivery worldwide. Bestselling Series. Harry Potter. Popular Features. Home Learning. Description This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle In addition, it contains a wealth of problems and exercises with solutions to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations PDEs.
Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. The English edition makes a welcome addition to this list. Product details Format Paperback pages Dimensions x x Other books in this series. Add to basket. Algebra Serge Lang. An Introduction to Manifolds Loring W. Ordinary Differential Equations Vladimir I. Mathematical Analysis I Vladimir A. Probability Essentials Jean Jacod.
Probability Theory Achim Klenke. Differential Forms and Applications Manfredo P. Complex Analysis Eberhard Freitag. Introduction to Homotopy Theory Martin Arkowitz. Logic and Structure Dirk Van Dalen. Geometric Group Theory Clara Loeh. Back cover copy Uniquely, this book presents a coherent, concise and unified way of combining elements from two distinct "worlds," functional analysis FA and partial differential equations PDEs , and is intended for students who have a good background in real analysis.
Moreover, the wealth of exercises and additional material presented, leads the reader to the frontier of research. This book has its roots in a celebrated course taught by the author for many years and is a completely revised, updated, and expanded English edition of the important "Analyse Fonctionnelle" The English version is a welcome addition to this list. The first part of the text deals with abstract results in FA and operator theory.
The second part is concerned with the study of spaces of functions of one or more real variables having specific differentiability properties, e. The Sobolev spaces occur in a wide range of questions, both in pure and applied mathematics, appearing in linear and nonlinear PDEs which arise, for example, in differential geometry, harmonic analysis, engineering, mechanics, physics etc.
Table of contents Preface. The Hahn-Banach Theorems. Introduction to the Theory of Conjugate Convex Functions. Unbounded Operators. Characterization of Surjective Operators. Weak Topologies. Reflexive Spaces. Separable Spaces. Uniform Convexity. Hilbert Spaces.
Compact Operators. The Hille-Yosida Theorem. Some Complements. Review Text From the reviews: "Brezis has intelligently chosen several fundamental concepts of functional analysis, and has build the book around them and their applications. In fact I would recommend this over any other source to any beginning graduate student. Its a bible for the field of research. At the end of each chapter the reader will find comments with further information, references, and historic remarks.
In summary, the present textbook provides an excellent basis for a course on functional analysis plus a follow-up course on partial differential equations. It is well-written and I can wholeheartedly recommend it to both students and teachers. The writing is lively, the material is diverse and maintains a strong unity. I wholeheartedly recommend this book both as a textbook, as well as for independent study.
It has seen translations into numerous languages and the Springer edition was especially anticipated, as it announced a number of practice exercises following each chapter. I can honestly say that it was well worth the wait. The text is a pleasure to read.
I wholeheartedly recommend this book as both a textbook as well as for independent study. Review quote From the reviews: "Brezis has intelligently chosen several fundamental concepts of functional analysis, and has build the book around them and their applications. Teschl, Monatshefte fur Mathematik, Vol. Rating details. Book ratings by Goodreads.
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Functional Analysis, Sobolev Spaces and Partial Differential Equations