Integral Transforms Of Generalized Functions

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Integral Transforms of Generalized Functions

Author : Brychkov
Publisher : CRC Press
ISBN 13 : 9782881247057
Total Pages : 362 pages
Book Rating : 4.2/5 (47 download)

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Book Synopsis Integral Transforms of Generalized Functions by : Brychkov

Download or read book Integral Transforms of Generalized Functions written by Brychkov and published by CRC Press. This book was released on 1989-04-20 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: English translation (from revised and enlarged versions of the Russian editions of 1977 and 1984) of a reference work which makes available to engineers, physicists and applied mathematicians theoretical and tabular material pertaining to certain extensions of standard integral transform techniques. Diverse transforms are touched upon, but the emphasis (particularly in the tables) is on generalized Fourier and Laplace transforms. Some multi-dimensional results are presented. Expensive, but nicely produced, and redundant with nothing standard to the reference shelves of mathematical libraries. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Integral Transforms of Generalized Functions and Their Applications

Author : Ram Shankar Pathak
Publisher : Routledge
ISBN 13 : 135156269X
Total Pages : 432 pages
Book Rating : 4.3/5 (515 download)

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Book Synopsis Integral Transforms of Generalized Functions and Their Applications by : Ram Shankar Pathak

Download or read book Integral Transforms of Generalized Functions and Their Applications written by Ram Shankar Pathak and published by Routledge. This book was released on 2017-07-05 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integral Transformations, Operational Calculus, and Generalized Functions

Author : R.G. Buschman
Publisher : Springer Science & Business Media
ISBN 13 : 1461312833
Total Pages : 248 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Integral Transformations, Operational Calculus, and Generalized Functions by : R.G. Buschman

Download or read book Integral Transformations, Operational Calculus, and Generalized Functions written by R.G. Buschman and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is not the object of the author to present comprehensive cov erage of any particular integral transformation or of any particular development of generalized functions, for there are books available in which this is done. Rather, this consists more of an introductory survey in which various ideas are explored. The Laplace transforma tion is taken as the model type of an integral transformation and a number of its properties are developed; later, the Fourier transfor mation is introduced. The operational calculus of Mikusinski is pre sented as a method of introducing generalized functions associated with the Laplace transformation. The construction is analogous to the construction of the rational numbers from the integers. Further on, generalized functions associated with the problem of extension of the Fourier transformation are introduced. This construction is anal ogous to the construction of the reals from the rationals by means of Cauchy sequences. A chapter with sections on a variety of trans formations is adjoined. Necessary levels of sophistication start low in the first chapter, but they grow considerably in some sections of later chapters. Background needs are stated at the beginnings of each chapter. Many theorems are given without proofs, which seems appro priate for the goals in mind. A selection of references is included. Without showing many of the details of rigor it is hoped that a strong indication is given that a firm mathematical foundation does actu ally exist for such entities as the "Dirac delta-function".

Integral Transforms of Generalized Functions and Their Application

Author : R.S. Pathak
Publisher :
ISBN 13 : 9782884492188
Total Pages : pages
Book Rating : 4.4/5 (921 download)

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Book Synopsis Integral Transforms of Generalized Functions and Their Application by : R.S. Pathak

Download or read book Integral Transforms of Generalized Functions and Their Application written by R.S. Pathak and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mortality

Author : Christopher Hitchens
Publisher : Allen & Unwin
ISBN 13 : 1742695191
Total Pages : 130 pages
Book Rating : 4.7/5 (426 download)

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Book Synopsis Mortality by : Christopher Hitchens

Download or read book Mortality written by Christopher Hitchens and published by Allen & Unwin. This book was released on 2012-09-01 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Courageous, insightful and candid thoughts on malady and mortality from one of our most celebrated writers.

Transform Analysis of Generalized Functions

Author : O.P. Misra
Publisher : Elsevier
ISBN 13 : 9780080872308
Total Pages : 331 pages
Book Rating : 4.8/5 (723 download)

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Book Synopsis Transform Analysis of Generalized Functions by : O.P. Misra

Download or read book Transform Analysis of Generalized Functions written by O.P. Misra and published by Elsevier. This book was released on 1986-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series. Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here. The volume will serve as introductory and reference material for those interested in analysis, applications, physics and engineering.

Fractional Calculus and Integral Transforms of Generalized Functions

Author : A. C. McBride
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Fractional Calculus and Integral Transforms of Generalized Functions by : A. C. McBride

Download or read book Fractional Calculus and Integral Transforms of Generalized Functions written by A. C. McBride and published by Pitman Publishing. This book was released on 1979 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Integral Transforms and their Applications

Author : B. Davies
Publisher : Springer Science & Business Media
ISBN 13 : 1489926917
Total Pages : 427 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Integral Transforms and their Applications by : B. Davies

Download or read book Integral Transforms and their Applications written by B. Davies and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In preparing this second edition I have restricted myself to making small corrections and changes to the first edition. Two chapters have had extensive changes made. First, the material of Sections 14.1 and 14.2 has been rewritten to make explicit reference to the book of Bleistein and Handelsman, which appeared after the original Chapter 14 had been written. Second, Chapter 21, on numerical methods, has been rewritten to take account of comparative work which was done by the author and Brian Martin, and published as a review paper. The material for all of these chapters was in fact, prepared for a transla tion of the book. Considerable thought has been given to a much more com prehensive revision and expansion of the book. In particular, there have been spectacular advances in the solution of some non-linear problems using isospectra1 methods, which may be re garded as a generalization of the Fourier transform. However, the subject is a large one, and even a modest introduction would have added substantially to the book. Moreover, the recent book by Dodd et al. is at a similar level to the present volume. Similarly, I have refrained from expanding the chapter on num erical methods into a complete new part of the book, since a specialized monograph on numerical methods is in preparation in collaboration with a colleague.

Methods of the Theory of Generalized Functions

Author : V. S. Vladimirov
Publisher : CRC Press
ISBN 13 : 9780415273565
Total Pages : 332 pages
Book Rating : 4.2/5 (735 download)

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Book Synopsis Methods of the Theory of Generalized Functions by : V. S. Vladimirov

Download or read book Methods of the Theory of Generalized Functions written by V. S. Vladimirov and published by CRC Press. This book was released on 2002-08-15 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.

Introduction to Hyperfunctions and Their Integral Transforms

Author : Urs Graf
Publisher : Springer Science & Business Media
ISBN 13 : 3034604076
Total Pages : 422 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Introduction to Hyperfunctions and Their Integral Transforms by : Urs Graf

Download or read book Introduction to Hyperfunctions and Their Integral Transforms written by Urs Graf and published by Springer Science & Business Media. This book was released on 2010-03-12 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents an introduction to the subject of generalized functions and their integral transforms by an approach based on the theory of functions of one complex variable. It includes many concrete examples.

Handbook of Function and Generalized Function Transformations

Author : Ahmed I. Zayed
Publisher : CRC Press
ISBN 13 : 0429605390
Total Pages : 684 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Handbook of Function and Generalized Function Transformations by : Ahmed I. Zayed

Download or read book Handbook of Function and Generalized Function Transformations written by Ahmed I. Zayed and published by CRC Press. This book was released on 2019-08-21 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems. The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included. The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations.

Applications of Fourier Transforms to Generalized Functions

Author : M. Rahman
Publisher : WIT Press
ISBN 13 : 1845645642
Total Pages : 193 pages
Book Rating : 4.8/5 (456 download)

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Book Synopsis Applications of Fourier Transforms to Generalized Functions by : M. Rahman

Download or read book Applications of Fourier Transforms to Generalized Functions written by M. Rahman and published by WIT Press. This book was released on 2011 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized function is one of the important branches of mathematics which has enormous applications in practical fields. In particular its applications to the theory of distribution and signal processing are very much essential. In this computer age, information science plays a very important role and the Fourier transform is extremely significant in deciphering obscured information to be made understandable. The book contains six chapters and three appendices. Chapter 1 deals with the preliminary remarks of Fourier series from general point of view. Chapter 2 is concerned with the generalized functions and their Fourier transforms. Chapter 3 contains the Fourier transforms of particular generalized functions. Chapter 4 deals with the asymptotic estimation of Fourier transforms. Chapter 5 is devoted to the study of Fourier series as a series of generalized functions. Chapter 6 deals with the fast Fourier transforms.Appendix A contains the extended list of Fourier transform pairs.Appendix B illustrates the properties of impulse function.Appendix C contains an extended list of biographical references

Generalized Integral Transforms In Mathematical Finance

Author : Andrey Itkin
Publisher : World Scientific
ISBN 13 : 9811231753
Total Pages : 508 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Generalized Integral Transforms In Mathematical Finance by : Andrey Itkin

Download or read book Generalized Integral Transforms In Mathematical Finance written by Andrey Itkin and published by World Scientific. This book was released on 2021-10-12 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model with default contagion; (c) finding first hitting time density for a reducible diffusion process; (d) describing the exercise boundary of American options; (e) calculating default boundary for the structured default problem; (f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.The main methods used in this book are generalized integral transforms and heat potentials. To find a semi-closed form solution, we need to solve a linear or nonlinear Volterra equation of the second kind and then represent the option price as a one-dimensional integral. Our analysis shows that these methods are computationally more efficient than the corresponding finite-difference methods for the backward or forward Kolmogorov PDEs (partial differential equations) while providing better accuracy and stability.We extend a large number of known results by either providing solutions on complementary or extended domains where the solution is not known yet or modifying these techniques and applying them to new types of equations, such as the Bessel process. The book contains several novel results broadly applicable in physics, mathematics, and engineering.

Handbook of Function and Generalized Function Transformations

Author : Ahmed I. Zayed
Publisher : CRC Press
ISBN 13 : 0429610912
Total Pages : 672 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Handbook of Function and Generalized Function Transformations by : Ahmed I. Zayed

Download or read book Handbook of Function and Generalized Function Transformations written by Ahmed I. Zayed and published by CRC Press. This book was released on 2019-08-21 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems. The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included. The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections:

Integral Transforms and Their Applications

Author : Lokenath Debnath
Publisher : CRC Press
ISBN 13 : 1420010913
Total Pages : 723 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Integral Transforms and Their Applications by : Lokenath Debnath

Download or read book Integral Transforms and Their Applications written by Lokenath Debnath and published by CRC Press. This book was released on 2016-04-19 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keeping the style, content, and focus that made the first edition a bestseller, Integral Transforms and their Applications, Second Edition stresses the development of analytical skills rather than the importance of more abstract formulation. The authors provide a working knowledge of the analytical methods required in pure and applied mathematics, physics, and engineering. The second edition includes many new applications, exercises, comments, and observations with some sections entirely rewritten. It contains more than 500 worked examples and exercises with answers as well as hints to selected exercises. The most significant changes in the second edition include: New chapters on fractional calculus and its applications to ordinary and partial differential equations, wavelets and wavelet transformations, and Radon transform Revised chapter on Fourier transforms, including new sections on Fourier transforms of generalized functions, Poissons summation formula, Gibbs phenomenon, and Heisenbergs uncertainty principle A wide variety of applications has been selected from areas of ordinary and partial differential equations, integral equations, fluid mechanics and elasticity, mathematical statistics, fractional ordinary and partial differential equations, and special functions A broad spectrum of exercises at the end of each chapter further develops analytical skills in the theory and applications of transform methods and a deeper insight into the subject A systematic mathematical treatment of the theory and method of integral transforms, the book provides a clear understanding of the subject and its varied applications in mathematics, applied mathematics, physical sciences, and engineering.

Asymptotic Behavior of Generalized Functions

Author : Stevan Pilipovic
Publisher : World Scientific
ISBN 13 : 9814366854
Total Pages : 309 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Asymptotic Behavior of Generalized Functions by : Stevan Pilipovic

Download or read book Asymptotic Behavior of Generalized Functions written by Stevan Pilipovic and published by World Scientific. This book was released on 2012 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach OCo of Estrada, Kanwal and Vindas OCo is related to moment asymptotic expansions of generalized functions and the Ces''aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.

Integral Transforms and Their Applications, Third Edition

Author : Lokenath Debnath
Publisher : CRC Press
ISBN 13 : 1482223570
Total Pages : 820 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Integral Transforms and Their Applications, Third Edition by : Lokenath Debnath

Download or read book Integral Transforms and Their Applications, Third Edition written by Lokenath Debnath and published by CRC Press. This book was released on 2014-11-07 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Transforms and Their Applications, Third Edition covers advanced mathematical methods for many applications in science and engineering. The book is suitable as a textbook for senior undergraduate and first-year graduate students and as a reference for professionals in mathematics, engineering, and applied sciences. It presents a systematic development of the underlying theory as well as a modern approach to Fourier, Laplace, Hankel, Mellin, Radon, Gabor, wavelet, and Z transforms and their applications. New to the Third Edition New material on the historical development of classical and modern integral transforms New sections on Fourier transforms of generalized functions, the Poisson summation formula, the Gibbs phenomenon, and the Heisenberg uncertainty principle Revised material on Laplace transforms and double Laplace transforms and their applications New examples of applications in mechanical vibrations, electrical networks, quantum mechanics, integral and functional equations, fluid mechanics, mathematical statistics, special functions, and more New figures that facilitate a clear understanding of physical explanations Updated exercises with solutions, tables of integral transforms, and bibliography Through numerous examples and end-of-chapter exercises, this book develops readers’ analytical and computational skills in the theory and applications of transform methods. It provides accessible working knowledge of the analytical methods and proofs required in pure and applied mathematics, physics, and engineering, preparing readers for subsequent advanced courses and research in these areas.