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Fractals and Spectra

Related to Fourier Analysis and Function Spaces

  • Hans Triebel

Part of the Modern Birkhäuser Classics book series

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

  • Hans Triebel
    • 1
  1. 1.Fak. Mathematik/Informatik, Inst. MathematikUniversität JenaJenaGermany

Bibliographic information

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