Hilbert Transforms

Volume 1

$181.00 (C)

Part of Encyclopedia of Mathematics and its Applications

Author: Frederick W. King, University of Wisconsin, Eau Claire

Date Published: April 2009
availability: Available
format: Hardback
isbn: 9780521887625

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Description

The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications.
- Informal style opens up the material to anyone working in the physical sciences
- The only book to contain an extensive table of Hilbert transforms, and it has a mini atlas to show reader immediately how the Hilbert transform alters a function
- Exercises are included to help test understanding, and a large bibliography points to classical papers and a wide range of applications
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Reviews & endorsements
"The author gives detailed and exhaustive information on almost all properties of the Hilbert transform... the selected topics are presented in an easy-to-use style."
Lasha Ephremidze, Mathematical Reviews

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Product details
- Date Published: April 2009
- format: Hardback
- isbn: 9780521887625
- length: 896 pages
- dimensions: 242 x 162 x 50 mm
- weight: 1.52kg
- contains: 15 tables 350 exercises
- availability: Available
Table of Contents
Preface
List of symbols
List of abbreviations
Volume I:
1. Introduction
2. Review of some background mathematics
3. Derivation of the Hilbert transform relations
4. Some basic properties of the Hilbert transform
5. Relationship between the Hilbert transform and some common transforms
6. The Hilbert transform of periodic functions
7. Inequalities for the Hilbert transform
8. Asymptotic behavior of the Hilbert transform
9. Hilbert transforms of some special functions
10. Hilbert transforms involving distributions
11. The finite Hilbert transform
12. Some singular integral equations
13. Discrete Hilbert transforms
14. Numerical evaluation of Hilbert transforms
References
Subject index
Author index.
Look Inside
Author
Frederick W. King, University of Wisconsin, Eau Claire
Frederick W. King is a Professor in the Department of Chemistry at the University of Wisconsin-Eau Claire.