| eBook ISBN: | 978-1-4704-0172-6 |
| Product Code: | MEMO/123/587.E |
| List Price: | $45.00 |
| MAA Member Price: | $40.50 |
| AMS Member Price: | $27.00 |
| eBook ISBN: | 978-1-4704-0172-6 |
| Product Code: | MEMO/123/587.E |
| List Price: | $45.00 |
| MAA Member Price: | $40.50 |
| AMS Member Price: | $27.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 123; 1996; 110 ppMSC: 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.
ReadershipGraduate students and researchers in mathematics, physics, and engineering who are interested in wavelets.
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Table of Contents
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Chapters
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Introduction
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I. Modulus of continuity and two-microlocalization
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II. Singularities of functions in Sobolev spaces
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III. Wavelets and lacunary trigonometric series
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IV. Properties of chirp expansions
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V. Trigonometric chirps
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VI. Logarithmic chirps
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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 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.
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
