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The Structure of Functions

  • Book
  • © 2001


  • 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 years
  • 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?
  • Includes supplementary material:

Part of the book series: Modern Birkhäuser Classics (MBC)

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About this book

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)

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Table of contents (4 chapters)

Authors and Affiliations

  • , Mathematical Institute, Friedrich-Schiller-University Jena, Jena, Germany

    Hans Triebel

About the author

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

Bibliographic Information

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