Overview
- 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: sn.pub/extras
Part of the book series: Modern Birkhäuser Classics (MBC)
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Table of contents (4 chapters)
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
- distribution
- function space
- quark
- spectral theory
- wavelet
- partial differential equations
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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: The Structure of Functions
Authors: Hans Triebel
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-3-0348-0569-8
Publisher: Birkhäuser Basel
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eBook Packages: Springer Book Archive
Copyright Information: Springer Basel 2001
Softcover ISBN: 978-3-0348-0568-1Published: 14 December 2012
eBook ISBN: 978-3-0348-0569-8Published: 13 December 2012
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XII, 425
Additional Information: Originally published as volume 97 in the Monographs in Mathematics series
Topics: Functional Analysis, Measure and Integration, Abstract Harmonic Analysis, Partial Differential Equations, Operator Theory