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Functional Analysis : Fundamentals and Applications / by Michel Willem

By: Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: CornerstonesPublisher: Cham : Springer International Publishing, 2022Publisher: Cham : Imprint: Birkhäuser, 2022Edition: 2nd ed. 2022Description: 1 Online-Ressource(XV, 251 p. 3 illus.)ISBN:
  • 9783031091490
Subject(s): Additional physical formats: 9783031091483 | 9783031091506 | 9783031091513 | Erscheint auch als: 9783031091483 Druck-Ausgabe | Erscheint auch als: 9783031091506 Druck-Ausgabe | Erscheint auch als: 9783031091513 Druck-Ausgabe | Erscheint auch als: Functional analysis. Druck-Ausgabe Second edition. Cham : Birkhäuser, 2022. xv, 251 SeitenDDC classification:
  • 515.7 23
DOI: DOI: 10.1007/978-3-031-09149-0Online resources: Summary: Preface -- Distance -- The Integral -- Norms -- Lebesgue Spaces -- Duality -- Sobolev Spaces.-Capacity -- Elliptic Problems -- Appendix: Topics in Calculus -- Epilogue: Historical Notes on Functional Analysis.Summary: 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.PPN: PPN: 1832786013Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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