Linear and Nonlinear Functional Analysis with Applications
By: Philippe G. Ciarlet (author)Paperback
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Functional analysis occupies a central position in modern mathematics, and has powerful applications in many other branches of the subject. This book provides a thorough and self-contained introduction to the basic aspects of both linear and nonlinear functional analysis. Most of the major results are accompanied by complete proofs, and illustrated with a variety of applications to numerical analysis, optimisation theory, and partial differential equations. As well as covering a vast amount of foundational material, historical notes and many original references are included to help the reader explore the genesis of some important results. This book is intended for advanced undergraduates, graduate students, and researchers. With illustrations and over 400 problems, it is ideal for both teaching and self-study.
Philippe G. Ciarlet began his academic career at the Universite Pierre et Marie Curie, Paris, in 1974, and moved to the City University of Hong Kong in 2002. He is a member of eight academies, including the French Academy of Sciences and the Hong Kong Institution of Science, and is a Fellow of SIAM and the AMS. Ciarlet is the recipient of a Grand Prize from the French Academy of Sciences and a Humboldt Research Award, as well as many other awards. He is Doctor Honoris Causa, or Honorary Professor, at eight universities and the author of 190 research papers and fifteen books.
Preface; 1. Real analysis and theory of functions: a quick review; 2. Normed vector spaces; 3. Banach spaces; 4. Inner-product spaces and Hilbert spaces; 5. The 'great theorems' of linear functional analysis; 6. Linear partial differential equations; 7. Differential calculus in normed vector spaces; 8. Differential geometry in Rn; 9. The 'great theorems' of nonlinear functional analysis; Bibliographical notes; Bibliography; Main notations; Index.
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- ID: 9781611972580
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