ENGLISH

Functional Analysis: Fundamentals and Applications

By Michel Willem (auth.)

Book information

Publisher
Birkhäuser Basel
Year
2013
ISBN
978-1-4614-7003-8, 978-1-4614-7004-5
DOI
10.1007/978-1-4614-7004-5
Language
english
Format
PDF
Filesize
1 MB (1313316 bytes)
Series
Cornerstones
Edition
1
Pages
213\220
Orientation
yes
Scanned
yes
Time added
2013-08-12 07:15:11
Functional Analysis; Analysis; Partial Differentiageneral

Description

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.

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