Willem Functional Analysis

Fundamentals and Applications
2. Auflage 2022
ISBN: 978-3-031-09149-0
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 251 Seiten, eBook

Reihe: 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-Szego 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.

Zielgruppe

Graduate

Autoren/Hrsg.

Willem, Michel

Inhaltsverzeichnis

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

Über Autor(innen)

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