TY  - BOOK
AU  - Willem,Michel
ED  - SpringerLink (Online service)
TI  - Functional Analysis: Fundamentals and Applications 
T2  - Cornerstones,
SN  - 9781461470045
AV  - QA319-329.9 
U1  - 515.7 23
PY  - 2013///
CY  - New York, NY
PB  - Springer New York, Imprint: Birkhäuser
KW  - Mathematics
KW  - Mathematical analysis
KW  - Analysis (Mathematics)
KW  - Functional analysis
KW  - Partial differential equations
KW  - Functional Analysis
KW  - Analysis
KW  - Partial Differential Equations
KW  - Mathematics, general
N1  - Preface -- The Integral -- Norm -- Lebesgue Spaces -- Duality -- Sobolev Spaces -- Capacity -- Elliptic Problems -- Appendix -- Epilogue -- References -- Index of Notations -- Index
N2  - 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
UR  - http://dx.doi.org/10.1007/978-1-4614-7004-5
ER  -