Functional Analysis: Fundamentals and Applications (Cornerstones)

Book Details

• Publisher: Birkhäuser

• Author: Michel Willem

• Language: English

• Edition: 2nd ed. 2022

• ISBN: 9783031091513

• Pages: 251

• Cover: Paperback

• Dimensions: 9.3 x 6.1 x 0.6 inches

About The Book

Functional Analysis (2nd ed.) by Michel Willem provides a clear and concise introduction to the principles of functional analysis. The textbook begins by covering the fundamental concepts of distance, integrals, and norms, establishing the foundational relationships between them. Through the first few chapters, the book explores key topics such as Lebesgue spaces, dual spaces, and Sobolev spaces, offering detailed examples to enhance understanding.

The text goes on to develop applications of functional analysis to capacity theory and elliptic problems, providing proofs of important inequalities like the isoperimetric inequality, Pólya-Szegő inequality, and Faber-Krahn inequality using purely functional methods. These applications highlight the power of functional analysis in solving real-world mathematical problems.

The second edition of this book includes substantial updates, particularly in the coverage of advanced calculus and distribution theory, which have been completely rewritten and expanded. New proofs, theorems, and applications have been added to provide readers with a deeper exploration of the subject.

This work is an excellent resource for students in mathematics and applied mathematics, particularly those interested in the theoretical foundations and applications of functional analysis. It serves as an accessible and rigorous guide, making it an invaluable textbook for both learning and reference in the field of functional analysis.