The structure of functions
著者
書誌事項
The structure of functions
（Modern Birkhäuser classics）
Birkhäuser, c2001
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注記
"Reprint of the 1st edition 2001 by Birkhäuser Verlag, Switzerland. Originally published as volume 97 in the Monographs Mathematics series"--T.p. verso
Includes references (p. 403-417), symbols and index
内容説明・目次
内容説明
This book deals with the constructive Weierstrassian approach to the theory of function spaces and various applications. The first chapter is devoted to a detailed study of quarkonial (subatomic) decompositions of functions and distributions on euclidean spaces, domains, manifolds and fractals. This approach combines the advantages of atomic and wavelet representations. It paves the way to sharp inequalities and embeddings in function spaces, spectral theory of fractal elliptic operators, and a regularity theory of some semi-linear equations.
The book is self-contained, although some parts may be considered as a continuation of the author's book Fractals and Spectra. It is directed to mathematicians and (theoretical) physicists interested in the topics indicated and, in particular, how they are interrelated.
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The book under review can be regarded as a continuation of [his book on "Fractals and spectra", 1997] (...) There are many sections named: comments, preparations, motivations, discussions and so on. These parts of the book seem to be very interesting and valuable. They help the reader to deal with the main course.
(Mathematical Reviews)
目次
Preface.- I Decompositions of Functions.- II Sharp Inequalities.- III Fractal Elliptic Operators.- IV Truncations and Semi-linear Equations.- References.- Symbols.- Index.
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