Functional Analysis

Fundamentals and Applications

Michel Willem

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Hardback

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English

Birkhauser Verlag AG
28 January 2023

Functional analysis & transforms

Series: Cornerstones

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.

By: Michel Willem
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: 2nd ed. 2022
Dimensions: Height: 235mm, Width: 155mm,
Weight: 571g
ISBN: 9783031091483
ISBN 10: 3031091485
Series: Cornerstones
Pages: 251
Publication Date: 28 January 2023
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Preface.- Distance.- The Integral.- Norms.- Lebesgue Spaces.- Duality.- Sobolev Spaces.-Capacity.- Elliptic Problems.- Appendix: Topics in Calculus.- Epilogue: Historical Notes on Functional Analysis.

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