01999nam a22003135i 450099100426623850753620240319102338.0230306s2013 nyu er 001 0 eng d9781489987945Bibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng510LC QA319-329.9AMS 46-01AMS 46B25Willem, Michel344839Functional analysis :fundamentals and applications /Michel WillemNew York, NY :Springer,2013xiii, 213 p. ;24 cmtexttxtCornerstones,2197-182XPreface -- The Integral -- Norm -- Lebesgue Spaces -- Duality -- Sobolev Spaces -- Capacity -- Elliptic Problems -- Appendix -- Epilogue -- References -- Index of Notations -- IndexThe 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 mathematicsFunctional analysisMathematical analysisAnalysis (Mathematics)Partial differential equations991004266238507536Functional Analysis2517706UNISALENTO