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

Pandey, J. N.

Hardcover

ISBN 10: 0471033731 ISBN 13: 9780471033738

Verlag: Wiley-Interscience, 1996

Inhaltsangabe

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, high-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

Über diesen Titel

Über die Autorin bzw. den Autor

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.

Von der hinteren Coverseite

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

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

Details zur Ausgabe

• Verlag: Wiley-Interscience
• Erscheinungsdatum: 1996
• Sprache: Englisch
• ISBN 10: 0471033731
• ISBN 13: 9780471033738
• Einband: Gebundene Ausgabe
• Auflage: 1
• Anzahl der Seiten: 288
• Kontakt zum Hersteller: Wiley-VCH GmbH; product_safety@wiley.com; ; Boschstrasse 12; Weinheim; 69469; Deutschland