Functional Analysis: Fundamentals and Applications (Cornerstones)

Willem, Michel

ISBN 10: 3031091515 / ISBN 13: 9783031091513

Published by Birkhäuser, 2024

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Bibliographic Details

• Title: Functional Analysis: Fundamentals and Applications (Cornerstones)
• Publisher: Birkhäuser
• Publication Date: 2024
• Language: English
• ISBN 10: 3031091515
• ISBN 13: 9783031091513
• Binding: Soft cover
• Edition: 2nd Edition
• Condition: New

About this title

Synopsis

This textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the three chapters that follow: Lebesgue spaces, dual spaces, and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szegő and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional  analysis in relation to integration and differentiation. Starting from elementary analysis and introducing relevant research, this work is an excellent resource for students in mathematics and applied mathematics.

The second edition of Functional Analysis includes several improvements as well as the addition of supplementary material. Specifically, the coverage of advanced calculus and distribution theory has been completely rewritten and expanded. New proofs, theorems, and applications have been added as well for readers to explore.

About the Author

Michel Willem is Full Professor Emeritus at ​Université catholique de Louvain, Belgium.