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The Hilbert Transform of Schwartz Distributions and Applications

J. N. Pandey

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Description for The Hilbert Transform of Schwartz Distributions and Applications Hardcover. This book covers the Hilbert transform of distribution and the space of periodic distributions with period. It includes inversion formulas worked out for the Hilbert transform and applied to solve singular integral equation occurring in elasticity and elsewhere. Series: Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts. Num Pages: 262 pages, Illustrations. BIC Classification: PBKF; PBKL. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 243 x 166 x 22. Weight in Grams: 566.
This book provides a modern and up-to-date treatment of the Hilberttransform of distributions and the space of periodic distributions.Taking a simple and effective approach to a complex subject, thisvolume is a first-rate textbook at the graduate level as well as anextremely useful reference for mathematicians, applied scientists,and engineers.

The author, a leading authority in the field, shares with thereader many new results from his exhaustive research on the Hilberttransform of Schwartz distributions. He describes in detail how touse the Hilbert transform to solve theoretical and physicalproblems in a wide range of disciplines; these include aerofoilproblems, dispersion relations, ... Read morehigh-energy physics, potentialtheory problems, and others.

Innovative at every step, J. N. Pandey provides a new definitionfor the Hilbert transform of periodic functions, which isespecially useful for those working in the area of signalprocessing for computational purposes. This definition could alsoform the basis for a unified theory of the Hilbert transform ofperiodic, as well as nonperiodic, functions.

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

Placing a strong emphasis on easy application of theory andtechniques, the book generalizes the Hilbert problem in higherdimensions and solves it in function spaces as well as ingeneralized function spaces. It simplifies the one-dimensionaltransform of distributions; provides solutions to thedistributional Hilbert problems and singular integral equations;and covers the intrinsic definition of the testing function spacesand its topology.

The book includes exercises and review material for all majortopics, and incorporates classical and distributional problems intothe main text. Thorough and accessible, it explores new ways to usethis important integral transform, and reinforces its value in bothmathematical research and applied science.

The Hilbert transform made accessible with many new formulas anddefinitions

Written by today's foremost expert on the Hilbert transform ofgeneralized functions, this combined text and reference covers theHilbert transform of distributions and the space of periodicdistributions. The author provides a consistently accessibletreatment of this advanced-level subject and teaches techniquesthat can be easily applied to theoretical and physical problemsencountered by mathematicians, applied scientists, and graduatestudents in mathematics and engineering.

Introducing many new inversion formulas that have been developedand applied by the author and his research associates, the book:
* Provides solutions to the distributional Hilbert problem andsingular 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 importanttheoretical results of importance to research mathematicians
* Provides the characterization of functions and generalizedfunctions whose Fourier transforms are supported in certainorthants of Rn
* Offers a new definition of the Hilbert transform of the periodicfunction that can be used for computational purposes in signalprocessing
* Develops the theory of the Hilbert transform of periodicdistributions and the approximate Hilbert transform of periodicdistributions
* Provides exercises at the end of each chapter--useful toprofessors in planning assignments, tests, and problems Show Less

Product Details

Format

Hardback

Publication date

1995

Publisher

John Wiley and Sons Ltd United States

Number of pages

262

Condition

New

Series

Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts

Number of Pages

280

Place of Publication

, United States

ISBN

9780471033738

SKU

V9780471033738

Shipping Time

Usually ships in 7 to 11 working days

Ref

99-50

About J. N. Pandey

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.

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J. N. Pandey

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