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Probabilistic and Stochastic Methods in Analysis, with Applications

  • Book
  • © 1992

Overview

Editors:
  1. J. S. Byrnes

    1. Prometheus Inc., Newport, USA
      University of Massachusetts, Boston, USA

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  2. Jennifer L. Byrnes

    1. Harvard University, Cambridge, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Kathryn A. Hargreaves

    1. Prometheus Inc., Newport, USA
      Free Software Foundation, Cambridge, USA

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    You can also search for this editor in PubMed   Google Scholar

  4. Karl Berry

    1. Prometheus Inc., Newport, USA
      Free Software Foundation, Cambridge, USA

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Part of the book series: Nato Science Series C: (ASIC, volume 372)

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Table of contents (35 chapters)

  1. Front Matter

    Pages i-xi
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  2. Wavelets and fractals

    1. Front Matter

      Pages 1-1
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    2. Wavelets and analysis of partial differential equations

      • Stéphane Jaffard
      Pages 3-13

    3. Methods of solving dilation equations

      • Christopher Heil
      Pages 15-45

    4. Characterization of singularities

      • Stéphane Mallat, Wen Liang Hwang
      Pages 47-100

    5. Complex analysis and frames in sampling theory

      • William Heller
      Pages 101-116

    6. Stationary frames and spectral estimation

      • John J. Benedetto
      Pages 117-161

    7. Density of fuzzy attractors: A step towards the solution of the inverse problem for fractals and other sets

      • Carlos Cabrelli, Ursula Molter
      Pages 163-173

    8. Multifractal measures

      • Jacques Peyrière
      Pages 175-186

    9. Applications of Gabor and wavelet expansions to the Radon transform

      • David Walnut
      Pages 187-205

    10. Normal numbers and dynamical systems

      • Gavin Brown
      Pages 207-216

    11. Linear and non-linear decomposition of images using Gabor wavelets

      • Bruce W. Suter, Matthew Kabrisky, Steven K. Rogers, Erik J. Fretheim, Dennis W. Ruck, Michael Mueller
      Pages 217-231

    12. Multiresolution analyses, tiles, and scaling functions

      • W. R. Madych
      Pages 233-243
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Keywords

About this book

Probability has been an important part of mathematics for more than three centuries. Moreover, its importance has grown in recent decades, since the computing power now widely available has allowed probabilistic and stochastic techniques to attack problems such as speech and image processing, geophysical exploration, radar, sonar, etc. -- all of which are covered here.
The book contains three exceptionally clear expositions on wavelets, frames and their applications. A further extremely active current research area, well covered here, is the relation between probability and partial differential equations, including probabilistic representations of solutions to elliptic and parabolic PDEs. New approaches, such as the PDE method for large deviation problems, and stochastic optimal control and filtering theory, are beginning to yield their secrets. Another topic dealt with is the application of probabilistic techniques to mathematical analysis. Finally, there are clear explanations of normal numbers and dynamic systems, and the influence of probability on our daily lives.

Editors and Affiliations

  • Prometheus Inc., Newport, USA

    J. S. Byrnes, Kathryn A. Hargreaves, Karl Berry

  • University of Massachusetts, Boston, USA

    J. S. Byrnes

  • Harvard University, Cambridge, USA

    Jennifer L. Byrnes

  • Free Software Foundation, Cambridge, USA

    Kathryn A. Hargreaves, Karl Berry

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