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Functional analysisfundamentals and applications /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Functional analysisby Michel Willem.
其他題名:	fundamentals and applications /
作者:	Willem, Michel.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xv, 251 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Functional analysis.
電子資源:	https://doi.org/10.1007/978-3-031-09149-0
ISBN:	9783031091490$q(electronic bk.)

Functional analysisfundamentals and applications /
Willem, Michel.

Functional analysisfundamentals and applications /[electronic resource] :by Michel Willem. - Second edition. - Cham :Springer International Publishing :2022. - xv, 251 p. :ill., digital ;24 cm. - Cornerstones,2197-1838. - Cornerstones..

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

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.

ISBN: 9783031091490$q(electronic bk.)

Standard No.: 10.1007/978-3-031-09149-0doiSubjects--Topical Terms:

200585
Functional analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

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520 $a 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.
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