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＜電子ブック＞
Functional Analysis : Fundamentals and Applications / by Michel Willem
(Cornerstones. ISSN:21971838)

版	1st ed. 2013.
出版者	(New York, NY : Springer New York : Imprint: Birkhäuser)
出版年	2013
本文言語	英語
大きさ	XIII, 213 p. 18 illus : online resource
著者標目	*Willem, Michel author SpringerLink (Online service)
件　名	LCSH:Functional analysis LCSH:Mathematical analysis LCSH:Differential equations LCSH:Mathematics FREE:Functional Analysis FREE:Analysis FREE:Differential Equations FREE:Mathematics
一般注記	Preface -- The Integral -- Norm -- Lebesgue Spaces -- Duality -- Sobolev Spaces -- Capacity -- Elliptic Problems -- Appendix -- Epilogue -- References -- Index of Notations -- Index The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: 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 with integration and differentiation. Starting from elementary analysis and introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics HTTP:URL=https://doi.org/10.1007/978-1-4614-7004-5

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