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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:

The Hilbert Transform of Schwartz Distributions and Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

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The Hilbert Transform of Schwartz Distributions and Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) Cover

 

Synopses & Reviews

Publisher Comments:

This book provides a modern and up-to-date treatment of the Hilbert transform of distributions and the space of periodic distributions. Taking a simple and effective approach to a complex subject, this volume is a first-rate textbook at the graduate level as well as an extremely useful reference for mathematicians, applied scientists, and engineers.

The author, a leading authority in the field, shares with the reader many new results from his exhaustive research on the Hilbert transform of Schwartz distributions. He describes in detail how to use the Hilbert transform to solve theoretical and physical problems in a wide range of disciplines; these include aerofoil problems, dispersion relations, high-energy physics, potential theory problems, and others.

Innovative at every step, J. N. Pandey provides a new definition for the Hilbert transform of periodic functions, which is especially useful for those working in the area of signal processing for computational purposes. This definition could also form the basis for a unified theory of the Hilbert transform of periodic, as well as nonperiodic, functions.

The Hilbert transform and the approximate Hilbert transform of periodic functions are worked out in detail for the first time in book form and can be used to solve Laplace's equation with periodic boundary conditions. Among the many theoretical results proved in this book is a Paley-Wiener type theorem giving the characterization of functions and generalized functions whose Fourier transforms are supported in certain orthants of Rn.

Placing a strong emphasis on easy application of theory and techniques, the book generalizes the Hilbert problem in higher dimensions and solves it in function spaces as well as in generalized function spaces. It simplifies the one-dimensional transform of distributions; provides solutions to the distributional Hilbert problems and singular integral equations; and covers the intrinsic definition of the testing function spaces and its topology.

The book includes exercises and review material for all major topics, and incorporates classical and distributional problems into the main text. Thorough and accessible, it explores new ways to use this important integral transform, and reinforces its value in both mathematical research and applied science.

The Hilbert transform made accessible with many new formulas and definitions

Written by today's foremost expert on the Hilbert transform of generalized functions, this combined text and reference covers the Hilbert transform of distributions and the space of periodic distributions. The author provides a consistently accessible treatment of this advanced-level subject and teaches techniques that can be easily applied to theoretical and physical problems encountered by mathematicians, applied scientists, and graduate students in mathematics and engineering.

Introducing many new inversion formulas that have been developed and applied by the author and his research associates, the book:

  • Provides solutions to the distributional Hilbert problem and singular integral equations
  • Focuses on the Hilbert transform of Schwartz distributions, giving intrinsic definitions of the space H(D) and its topology
  • Covers the Paley-Wiener theorem and provides many important theoretical results of importance to research mathematicians
  • Provides the characterization of functions and generalized functions whose Fourier transforms are supported in certain orthants of Rn
  • Offers a new definition of the Hilbert transform of the periodic function that can be used for computational purposes in signal processing
  • Develops the theory of the Hilbert transform of periodic distributions and the approximate Hilbert transform of periodic distributions
  • Provides exercises at the end of each chapter—useful to professors in planning assignments, tests, and problems

Book News Annotation:

A textbook for graduate courses and a reference for mathematicians, applied scientists, and engineers. Provides a current treatment of the Hilbert transform of distributions and the space of periodic distributions, drawing on Pandey's (mathematics, Carlton U., Ottawa) own research to explain how to use the transform to solve theoretical and physical problems in a wide range of disciplines.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Description:

Includes bibliographical references (p. 249-253) and indexes.

About the Author

J. N. PANDEY is Professor of Mathematics at Carleton University in Ottawa with over thirty years' experience in the field. He has been involved in many research projects, supervised doctoral candidates, and has published and reviewed numerous papers in North American and European professional journals.

Table of Contents

The Riemann-Hilbert Problem.

The Hilbert Transform of Distributions in D'Lp, 1 p infinity .

The Hilbert Transform of Schwartz Distributions.

n-Dimensional Hilbert Transform.

Further Applications of the Hilbert Transform, the Hilbert Problem-- A Distributional Approach.

Periodic Distributions, Their Hilbert Transform and Applications.

Bibliography.

Indexes.

Product Details

ISBN:
9780471033738
Author:
Pandey, J. N.
Publisher:
Wiley-Interscience
Location:
New York :
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Functional Analysis
Subject:
Transformations (mathematics)
Subject:
Schwartz distributions.
Subject:
Hilbert transform.
Subject:
Mathematics-Analysis General
Subject:
Complex & Functional Analysis
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Series Volume:
27
Publication Date:
December 1995
Binding:
HARDCOVER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
262
Dimensions:
244 x 162 x 23 mm 20 oz

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Related Subjects


Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry

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