Distribution Integral Transforms And Applications
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Distribution Integral Transforms And Applications
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Author : W. Kierat
language : en
Publisher: CRC Press
Release Date : 2003-01-16
Distribution Integral Transforms And Applications written by W. Kierat and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-16 with Mathematics categories.
The theory of distributions is most often presented as L. Schwartz originally presented it: as a theory of the duality of topological vector spaces. Although this is a sound approach, it can be difficult, demanding deep prior knowledge of functional analysis. The more elementary treatments that are available often consider distributions as limits o
Distribution Integral Transforms And Applications
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Author : Kierat
language : en
Publisher:
Release Date :
Distribution Integral Transforms And Applications written by Kierat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Distribution Integral Transforms And Applications
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Author : W. Kierat
language : en
Publisher: CRC Press
Release Date : 2003-01-16
Distribution Integral Transforms And Applications written by W. Kierat and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-16 with Mathematics categories.
The theory of distributions is most often presented as L. Schwartz originally presented it: as a theory of the duality of topological vector spaces. Although this is a sound approach, it can be difficult, demanding deep prior knowledge of functional analysis. The more elementary treatments that are available often consider distributions as limits of sequences of functions, but these usually present the theoretical foundations in a form too simplified for practical applications. Distributions, Integral Transforms and Applications offers an approachable introduction to the theory of distributions and integral transforms that uses Schwartz's description of distributions as linear continous forms on topological vector spaces. The authors use the theory of the Lebesgue integral as a fundamental tool in the proofs of many theorems and develop the theory from its beginnings to the point of proving many of the deep, important theorems, such as the Schwartz kernel theorem and the Malgrange-Ehrenpreis theorem. They clearly demonstrate how the theory of distributions can be used in cases such as Fourier analysis, when the methods of classical analysis are insufficient. Accessible to anyone who has completed a course in advanced calculus, this treatment emphasizes the remarkable connections between distributional theory, classical analysis, and the theory of differential equations and leads directly to applications in various branches of mathematics.
Distributions In The Physical And Engineering Sciences
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Author : Alexander I. Saichev
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-11-01
Distributions In The Physical And Engineering Sciences written by Alexander I. Saichev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-01 with Mathematics categories.
A comprehensive exposition on analytic methods for solving science and engineering problems, written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise.
A Guide To Distribution Theory And Fourier Transforms
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Author : Robert S. Strichartz
language : en
Publisher: World Scientific
Release Date : 2003
A Guide To Distribution Theory And Fourier Transforms written by Robert S. Strichartz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Distribution Theory
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Author : Petre Teodorescu
language : en
Publisher: John Wiley & Sons
Release Date : 2013-09-03
Distribution Theory written by Petre Teodorescu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-03 with Science categories.
In this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail. They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mechanics, as well as to problems pertaining to the mechanics of deformable solids and physics. Special attention is placed upon the introduction of corresponding mathematical models. Addressed to a wide circle of readers who use mathematical methods in their work: applied mathematicians, engineers in various branches, as well as physicists, while also benefiting students in various fields.
Integral Transforms Of Generalized Functions And Their Applications
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Author : Ram Shankar Pathak
language : en
Publisher: Routledge
Release Date : 2017-07-05
Integral Transforms Of Generalized Functions And Their Applications written by Ram Shankar Pathak and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-05 with History categories.
For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.
Distributions
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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-09
Distributions written by J.J. Duistermaat and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-09 with Mathematics categories.
This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.
The Hilbert Transform Of Schwartz Distributions And Applications
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Author : J. N. Pandey
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-14
The Hilbert Transform Of Schwartz Distributions And Applications written by J. N. Pandey and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-14 with Mathematics categories.
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
Transforms And Applications Handbook
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Author : Alexander D. Poularikas
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Transforms And Applications Handbook written by Alexander D. Poularikas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.