03701nam 22007815 450 991043803370332120200701020654.01-4614-7004-810.1007/978-1-4614-7004-5(CKB)3710000000015738(EBL)1394847(OCoLC)870244160(SSID)ssj0000988146(PQKBManifestationID)11544505(PQKBTitleCode)TC0000988146(PQKBWorkID)10950682(PQKB)11607002(DE-He213)978-1-4614-7004-5(MiAaPQ)EBC1394847(MiAaPQ)EBC6312586(Au-PeEL)EBL1394847(CaPaEBR)ebr10962442(PPN)172418771(EXLCZ)99371000000001573820130809d2013 u| 0engur|n|---|||||txtccrFunctional Analysis Fundamentals and Applications /by Michel Willem1st ed. 2013.New York, NY :Springer New York :Imprint: Birkhäuser,2013.1 online resource (220 p.)Cornerstones,2197-182XDescription based upon print version of record.1-4899-8794-0 1-4614-7003-X 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.Cornerstones,2197-182XFunctional analysisMathematical analysisAnalysis (Mathematics)Differential equations, PartialMathematicsFunctional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Mathematics, generalhttps://scigraph.springernature.com/ontologies/product-market-codes/M00009Functional analysis.Mathematical analysis.Analysis (Mathematics).Differential equations, Partial.Mathematics.Functional Analysis.Analysis.Partial Differential Equations.Mathematics, general.510Willem Michelauthttp://id.loc.gov/vocabulary/relators/aut344839MiAaPQMiAaPQMiAaPQBOOK9910438033703321Functional Analysis2517706UNINA