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Functional analysis = fundamentals and applications /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Functional analysis/ by 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

Functional analysis = fundamentals 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

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

672166
Functional Analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

Functional analysis = fundamentals and applications /
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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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