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Record Nr. |
UNINA9910438033703321 |
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Autore |
Willem Michel |
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Titolo |
Functional Analysis : Fundamentals and Applications / / by Michel Willem |
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Pubbl/distr/stampa |
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New York, NY : , : Springer New York : , : Imprint : Birkhäuser, , 2013 |
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ISBN |
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Edizione |
[1st ed. 2013.] |
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Descrizione fisica |
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1 online resource (220 p.) |
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Collana |
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Cornerstones, , 2197-182X |
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Disciplina |
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Soggetti |
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Functional analysis |
Mathematical analysis |
Analysis (Mathematics) |
Differential equations, Partial |
Mathematics |
Functional Analysis |
Analysis |
Partial Differential Equations |
Mathematics, general |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di contenuto |
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Preface -- The Integral -- Norm -- Lebesgue Spaces -- Duality -- Sobolev Spaces -- Capacity -- Elliptic Problems -- Appendix -- Epilogue -- References -- Index of Notations -- Index. |
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Sommario/riassunto |
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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 |
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introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics. |
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