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© 1997

Fractals and Spectra

Related to Fourier Analysis and Function Spaces

Book

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Hans Triebel
    Pages 1-32
  3. Hans Triebel
    Pages 33-48
  4. Hans Triebel
    Pages 49-123
  5. Hans Triebel
    Pages 125-197
  6. Back Matter
    Pages 260-271

About this book

Introduction

Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) the monograph presents in a self-contained and very readable and lively form a new, intriguing and potentially very useful chapter of the theory of pseudodifferential operators. - Mathematical Reviews The book deals with a very recent topic and presents the significant contributions of the author. It is directed to mathematicians interested in the interrelations between function spaces and fractal geometry and is also of interest for graduate students. - Operator Theory Reviews

Keywords

Eigenvalue Fourier analysis distribution entropy numbers fractal geometry function spaces functional analysis pseudodifferential operators

Authors and affiliations

  1. 1.Fak. Mathematik/Informatik, Inst. MathematikUniversität JenaJenaGermany

About the authors

Hans Triebel ist Professor der Mathematik an der Friedrich-Schiller-Universität Jena.

Bibliographic information

  • Book Title Fractals and Spectra
  • Book Subtitle Related to Fourier Analysis and Function Spaces
  • Authors Hans Triebel
  • Series Title Modern Birkhäuser Classics
  • DOI https://doi.org/10.1007/978-3-0348-0034-1
  • Copyright Information Birkhäuser Verlag 1997
  • Publisher Name Springer, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-5776-4
  • Softcover ISBN 978-3-0348-0033-4
  • eBook ISBN 978-3-0348-0034-1
  • Edition Number 1
  • Number of Pages VIII, 272
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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