Real and Functional Analysis. 1st ed. 2020

種類:

電子ブック

責任表示:

by Vladimir I. Bogachev, Oleg G. Smolyanov

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Bogachev, Vladimir I.
• Smolyanov, Oleg G.
• SpringerLink (Online service)

シリーズ名:

Moscow Lectures ; 4

ISBN:

9783030382193 [3030382192]    

注記:

Metric and Topological Spaces -- Fundamentals of Measure Theory -- The Lebesgue Integral -- Connections between the Integral and Derivative -- Normed and Euclidean Spaces -- Linear Operators and Functionals -- Spectral Theory -- Locally Convex Spaces and Distributions -- The Fourier Transform and Sobolev Spaces -- Unbounded Operators and Operator Semigroups -- Banach Algebras -- Infinite-Dimensional Analysis.
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.

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