Neuware -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.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)Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 440 pp. Englisch.

Bestandsnummer des Verk�ufers 9783034805681

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Bibliografische Details

Titel: The Structure of Functions
Verlag: Springer Basel, Birkh�user Basel Dez 2012
Ver�ffentlichungsdatum: 2012
Sprache: Englisch
ISBN-10: 3034805683
ISBN-13: 9783034805681
Bindung: Taschenbuch
Zustand: Neu

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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.

- - -

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)

�ber die Autorin bzw. den Autor

Hans Triebel was professor of mathematics at the Friedrich-Schiller-University Jena, Germany.

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