Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

The Uncertainty Principle in Harmonic Analysis

Authors: Havin, Victor, Jöricke, Burglind

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About this book

The present book is a collection of variations on a theme which can be summed up as follows: It is impossible for a non-zero function and its Fourier transform to be simultaneously very small. In other words, the approximate equalities x :::::: y and x :::::: fj cannot hold, at the same time and with a high degree of accuracy, unless the functions x and yare identical. Any information gained about x (in the form of a good approximation y) has to be paid for by a corresponding loss of control on x, and vice versa. Such is, roughly speaking, the import of the Uncertainty Principle (or UP for short) referred to in the title ofthis book. That principle has an unmistakable kinship with its namesake in physics - Heisenberg's famous Uncertainty Principle - and may indeed be regarded as providing one of mathematical interpretations for the latter. But we mention these links with Quantum Mechanics and other connections with physics and engineering only for their inspirational value, and hasten to reassure the reader that at no point in this book will he be led beyond the world of purely mathematical facts. Actually, the portion of this world charted in our book is sufficiently vast, even though we confine ourselves to trigonometric Fourier series and integrals (so that "The U. P. in Fourier Analysis" might be a slightly more appropriate title than the one we chose).

Table of contents (9 chapters)

  • Introduction

    Havin, Victor (et al.)

    Pages 1-7

  • Functions and Charges with Semibounded Spectra

    Havin, Victor (et al.)

    Pages 11-52

  • Some Topics Related to the Harmonic Analysis of Charges

    Havin, Victor (et al.)

    Pages 53-86

  • Hilbert Space Methods

    Havin, Victor (et al.)

    Pages 87-116

  • The Uncertainty Principle from the Complex Point of View. First Examples

    Havin, Victor (et al.)

    Pages 119-195

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-642-78377-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-3-642-78379-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Uncertainty Principle in Harmonic Analysis
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
28
Copyright
1994
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-78377-7
DOI
10.1007/978-3-642-78377-7
Softcover ISBN
978-3-642-78379-1
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XII, 547
Topics