Functional Analysis, Softcover reprint of the original 1st ed. 2013
Fundamentals and Applications
Cornerstones Series

Language: English

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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-Szeg? 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.

​Preface.- The Integral.- Norm.- Lebesgue Spaces.- Duality.- Sobolev Spaces.- Capacity.- Elliptic Problems.- Appendix.- Epilogue.- References.- Index of Notations.- Index.
Presents the principles of functional analysis in a clear and concise way Most competing titles are out of date Includes very recent simple proofs of the isoperimetric and the Faber-Krahn inequality, an elementary introduction to capacity theory, and a new perspective on the history of functional analysis ?