Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
 
St(’)ephane Jaffard CERMA-ENPC
Yves Meyer University of Paris IX
Front Cover for Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
Available Formats:
Electronic ISBN: 978-1-4704-0172-6
Product Code: MEMO/123/587.E
110 pp 
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
Front Cover for Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
Click above image for expanded view
  • Front Cover for Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
  • Back Cover for Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions
St(’)ephane Jaffard CERMA-ENPC
Yves Meyer University of Paris IX
Available Formats:
Electronic ISBN:  978-1-4704-0172-6
Product Code:  MEMO/123/587.E
110 pp 
List Price: $45.00
MAA Member Price: $40.50
AMS Member Price: $27.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1231996
    MSC: Primary 26; 42;



    Currently, new trends in mathematics are emerging from the fruitful interaction between signal processing, image processing, and classical analysis.

    One example is given by “wavelets”, which incorporate both the know-how of the Calderon-Zygmund school and the efficiency of some fast algorithms developed in signal processing (quadrature mirror filters and pyramidal algorithms.)

    A second example is “multi-fractal analysis”. The initial motivation was the study of fully developed turbulence and the introduction by Frisch and Parisi of the multi-fractal spectrum. Multi-fractal analysis provides a deeper insight into many classical functions in mathematics.

    A third example—“chirps”—is studied in this book. Chirps are used in modern radar or sonar technology. Once given a precise mathematical definition, chirps constitute a powerful tool in classical analysis.

    In this book, wavelet analysis is related to the 2-microlocal spaces discovered by J. M. Bony. The authors then prove that a wavelet based multi-fractal analysis leads to a remarkable improvement of Sobolev embedding theorem. In addition, they show that chirps were hidden in a celebrated Riemann series.

    Features:

    • Provides the reader with some basic training in new lines of research.
    • Clarifies the relationship between pointwise behavior and size properties of wavelet coefficents.

    Readership

    Graduate students and researchers in mathematics, physics, and engineering who are interested in wavelets.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • I. Modulus of continuity and two-microlocalization
    • II. Singularities of functions in Sobolev spaces
    • III. Wavelets and lacunary trigonometric series
    • IV. Properties of chirp expansions
    • V. Trigonometric chirps
    • VI. Logarithmic chirps
    • VII. The Riemann series
  • Request Review Copy
  • Get Permissions
Volume: 1231996
MSC: Primary 26; 42;



Currently, new trends in mathematics are emerging from the fruitful interaction between signal processing, image processing, and classical analysis.

One example is given by “wavelets”, which incorporate both the know-how of the Calderon-Zygmund school and the efficiency of some fast algorithms developed in signal processing (quadrature mirror filters and pyramidal algorithms.)

A second example is “multi-fractal analysis”. The initial motivation was the study of fully developed turbulence and the introduction by Frisch and Parisi of the multi-fractal spectrum. Multi-fractal analysis provides a deeper insight into many classical functions in mathematics.

A third example—“chirps”—is studied in this book. Chirps are used in modern radar or sonar technology. Once given a precise mathematical definition, chirps constitute a powerful tool in classical analysis.

In this book, wavelet analysis is related to the 2-microlocal spaces discovered by J. M. Bony. The authors then prove that a wavelet based multi-fractal analysis leads to a remarkable improvement of Sobolev embedding theorem. In addition, they show that chirps were hidden in a celebrated Riemann series.

Features:

  • Provides the reader with some basic training in new lines of research.
  • Clarifies the relationship between pointwise behavior and size properties of wavelet coefficents.

Readership

Graduate students and researchers in mathematics, physics, and engineering who are interested in wavelets.

  • Chapters
  • Introduction
  • I. Modulus of continuity and two-microlocalization
  • II. Singularities of functions in Sobolev spaces
  • III. Wavelets and lacunary trigonometric series
  • IV. Properties of chirp expansions
  • V. Trigonometric chirps
  • VI. Logarithmic chirps
  • VII. The Riemann series
Please select which format for which you are requesting permissions.