Originally published as volume 97 in the Monographs in Mathematics series
2001, XII, 425 p.
A product of Birkhäuser Basel
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Self-contained, i.e. the main ideas can be understood independently of the existing literature
Summarizes the results of the author and his co-workers in recent year
The material is presented in such a way that the main ideas can be understood independently of the existing literature
Addresses mathematicians and (theoretical) physicists
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)
Content Level »Research
Keywords »atomic and wavelet representations - embeddings in function spaces - quarkonial decompositions of functions and distributions - regularity theory of semi-linear equations - sharp inequalities - spectral theory of fractal elliptic operators