UID:
edocfu_9959327328502883
Format:
1 online resource (xvi, 262 pages).
ISBN:
9781118032510
,
1118032519
,
9781118030752
,
1118030753
Series Statement:
Pure and applied mathematics
Content:
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.
Content:
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 R[superscript n].
Content:
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.
Note:
Front Matter -- Some Background -- The Riemann-Hilbert Problem -- The Hilbert Transform of Distributions in D', 18 -- The Hilbert Transform of Schwartz Distributions --?-Dimensional Hilbert Transform -- Further Applications of the Hilbert Transform, the Hilbert Problem--A Distributional Approach -- Periodic Distributions, Their Hilbert Transform and Applications -- Bibliography -- Index -- Notation Index -- Pure and Applied Mathematics.
,
1. Some Background -- 2. The Riemann-Hilbert Problem -- 3. The Hilbert Transform of Distributions in [actual symbol not reproducible] -- 4. The Hilbert Transform of Schwartz Distributions -- 5. n-Dimensional Hilbert Transform -- 6. Further Applications of the Hilbert Transform, the Hilbert Problem -- A Distributional Approach -- 7. Periodic Distributions, Their Hilbert Transform and Applications.
Additional Edition:
Print version: Pandey, J.N. Hilbert transform of Schwartz distributions and applications. New York : Wiley, ©1996 ISBN 0471033731
Language:
English
Keywords:
Electronic books.
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118032510
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