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Presents the principles of functional analysis in a clear and concise way
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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
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.
Content Level »Graduate
Keywords »Banach spaces - Hilbert spaces - Lebesque spaces - Sobolev spaces - distribution theory - functional analysis