Functional Analysis - 9783031091513

Functional AnalysisFundamentals and Applications\nAuthor(s): Michel Willem\nFormat: Paperback\nPublisher: Birkhauser Verlag AG, Switzerland\nImprint: Birkhauser Verlag AG\nISBN-13: 9783031091513, 978-3031091513\nSynopsis\nThis textbook presents the principles of functional analysis in a clear and concise way. The first three chapters describe the general notions of distance, integral, and norm, as well as their relations. Fundamental examples are provided in the three chapters that follow: 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 Plya-Szeg? and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis in relation to integration and differentiation. Starting from elementary analysis and introducing relevant research, this work is an excellent resource for students.