Electronic ISBN:  9781470401726 
Product Code:  MEMO/123/587.E 
110 pp 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $27.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 123; 1996MSC: 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 knowhow of the CalderonZygmund school and the efficiency of some fast algorithms developed in signal processing (quadrature mirror filters and pyramidal algorithms.)
A second example is “multifractal analysis”. The initial motivation was the study of fully developed turbulence and the introduction by Frisch and Parisi of the multifractal spectrum. Multifractal 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 2microlocal spaces discovered by J. M. Bony. The authors then prove that a wavelet based multifractal 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.
ReadershipGraduate students and researchers in mathematics, physics, and engineering who are interested in wavelets.

Table of Contents

Chapters

Introduction

I. Modulus of continuity and twomicrolocalization

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


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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 knowhow of the CalderonZygmund school and the efficiency of some fast algorithms developed in signal processing (quadrature mirror filters and pyramidal algorithms.)
A second example is “multifractal analysis”. The initial motivation was the study of fully developed turbulence and the introduction by Frisch and Parisi of the multifractal spectrum. Multifractal 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 2microlocal spaces discovered by J. M. Bony. The authors then prove that a wavelet based multifractal 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.
Graduate students and researchers in mathematics, physics, and engineering who are interested in wavelets.

Chapters

Introduction

I. Modulus of continuity and twomicrolocalization

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