Multidimensional Integral Transformations
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Multidimensional Integral Transformations
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Author :
language : en
Publisher: CRC Press
Release Date : 1992
Multidimensional Integral Transformations written by and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
A cross between a textbook and a monograph, this extensive introduction discusses all of the most important transformations, compiling information otherwise scattered throughout the literature. Attention is concentrated on the operational calculus of the major integral transformations and some of its applications, with an investigation of transforms in spaces of functions and of distributions. Annotation copyrighted by Book News, Inc., Portland, OR
The Hypergeometric Approach To Integral Transforms And Convolutions
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Author : S.B. Yakubovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Hypergeometric Approach To Integral Transforms And Convolutions written by S.B. Yakubovich 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 2012-12-06 with Mathematics categories.
The aim of this book is to develop a new approach which we called the hyper geometric one to the theory of various integral transforms, convolutions, and their applications to solutions of integro-differential equations, operational calculus, and evaluation of integrals. We hope that this simple approach, which will be explained below, allows students, post graduates in mathematics, physicists and technicians, and serious mathematicians and researchers to find in this book new interesting results in the theory of integral transforms, special functions, and convolutions. The idea of this approach can be found in various papers of many authors, but systematic discussion and development is realized in this book for the first time. Let us explain briefly the basic points of this approach. As it is known, in the theory of special functions and its applications, the hypergeometric functions play the main role. Besides known elementary functions, this class includes the Gauss's, Bessel's, Kummer's, functions et c. In general case, the hypergeometric functions are defined as a linear combinations of the Mellin-Barnes integrals. These ques tions are extensively discussed in Chapter 1. Moreover, the Mellin-Barnes type integrals can be understood as an inversion Mellin transform from the quotient of products of Euler's gamma-functions. Thus we are led to the general construc tions like the Meijer's G-function and the Fox's H-function.
Handbook Of Mellin Transforms
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Author : Yu. A. Brychkov
language : en
Publisher: CRC Press
Release Date : 2018-10-10
Handbook Of Mellin Transforms written by Yu. A. Brychkov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-10 with Mathematics categories.
The Mellin transformation is widely used in various problems of pure and applied mathematics, in particular, in the theory of differential and integral equations and the theory of Dirichlet series. It is found in extensive applications in mathematical physics, number theory, mathematical statistics, theory of asymptotic expansions, and especially, in the theory of special functions and integral transformations. It is essentially used in algorithms of integration in computer algebra systems. Since the majority of integrals encountered in applications can be reduced to the form of the corresponding Mellin transforms with specific parameters, this handbook can also be used for definite and indefinite integrals. By changes in variables, the Mellin transform can be turned into the Fourier and Laplace transforms. The appendices contain formulas of connection with other integral transformations, and an algorithm for determining regions of convergence of integrals. The Handbook of Mellin Transforms will be of interest and useful to all researchers and engineers who use mathematical methods. It will become the main source of formulas of Mellin transforms, as well as indefinite and definite integrals.
Fractional Integrals Potentials And Radon Transforms
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Author : Boris Rubin
language : en
Publisher: CRC Press
Release Date : 2024-08-14
Fractional Integrals Potentials And Radon Transforms written by Boris Rubin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-14 with Mathematics categories.
Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how fractional integrals occur in the study of diverse Radon type transforms in integral geometry. Beyond some basic properties of fractional integrals in one and many dimensions, this book also contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaud’s approach and its generalization, leading to wavelet type representations. New to this Edition Two new chapters and a new appendix, related to Radon transforms and harmonic analysis of linear operators commuting with rotations and dilations have been added. Contains new exercises and bibliographical notes along with a thoroughly expanded list of references. This book is suitable for mathematical physicists and pure mathematicians researching in the area of integral equations, integral transforms, and related harmonic analysis.
Multidimensional Singular Integrals And Integral Equations
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Author : Solomon Grigorʹevich Mikhlin
language : en
Publisher:
Release Date : 1965
Multidimensional Singular Integrals And Integral Equations written by Solomon Grigorʹevich Mikhlin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Integral equations categories.
Applied Multidimensional Systems Theory
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Author : Nirmal K. Bose
language : en
Publisher: Springer
Release Date : 2016-12-24
Applied Multidimensional Systems Theory written by Nirmal K. Bose and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-24 with Technology & Engineering categories.
Revised and updated, this concise new edition of the pioneering book on multidimensional signal processing is ideal for a new generation of students. Multidimensional systems or m-D systems are the necessary mathematical background for modern digital image processing with applications in biomedicine, X-ray technology and satellite communications. Serving as a firm basis for graduate engineering students and researchers seeking applications in mathematical theories, this edition eschews detailed mathematical theory not useful to students. Presentation of the theory has been revised to make it more readable for students, and introduce some new topics that are emerging as multidimensional DSP topics in the interdisciplinary fields of image processing. New topics include Groebner bases, wavelets, and filter banks.
Index Transforms
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Author : Semyon B Yakubovich
language : en
Publisher: World Scientific
Release Date : 1996-02-29
Index Transforms written by Semyon B Yakubovich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-02-29 with Mathematics categories.
This book deals with the theory and some applications of integral transforms that involve integration with respect to an index or parameter of a special function of hypergeometric type as the kernel (index transforms). The basic index transforms are considered, such as the Kontorovich-Lebedev transform, the Mehler-Fock transform, the Olevskii Transform and the Lebedev-Skalskaya transforms. The Lp theory of index transforms is discussed, and new index transforms and convolution constructions are demonstrated. For the first time, the essentially multidimensional Kontorovich-Lebedev transform is announced. General index transform formulae are obtained. The connection between the multidimensional index kernels and G and H functions of several variables is presented. The book is self-contained, and includes a list of symbols with definitions, author and subject indices, and an up-to-date bibliography.This work will be of interest to researchers and graudate students in the mathematical and physical sciences whose work involves integral transforms and special functions.
The Double Mellin Barnes Type Integrals And Their Applications To Convolution Theory
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Author : Thanh Hai Nguyen
language : en
Publisher: World Scientific
Release Date : 1992
The Double Mellin Barnes Type Integrals And Their Applications To Convolution Theory written by Thanh Hai Nguyen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.
Methods For Solving Mathematical Physics Problems
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Author : Valeriĭ Ivanovich Agoshkov
language : en
Publisher: Cambridge Int Science Publishing
Release Date : 2006
Methods For Solving Mathematical Physics Problems written by Valeriĭ Ivanovich Agoshkov and has been published by Cambridge Int Science Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Science categories.
The aim of the book is to present to a wide range of readers (students, postgraduates, scientists, engineers, etc.) basic information on one of the directions of mathematics, methods for solving mathematical physics problems. The authors have tried to select for the book methods that have become classical and generally accepted. However, some of the current versions of these methods may be missing from the book because they require special knowledge. The book is of the handbook-teaching type. On the one hand, the book describes the main definitions, the concepts of the examined methods and approaches used in them, and also the results and claims obtained in every specific case. On the other hand, proofs of the majority of these results are not presented and they are given only in the simplest (methodological) cases. Another special feature of the book is the inclusion of many examples of application of the methods for solving specific mathematical physics problems of applied nature used in various areas of science and social activity, such as power engineering, environmental protection, hydrodynamics, elasticity theory, etc. This should provide additional information on possible applications of these methods. To provide complete information, the book includes a chapter dealing with the main problems of mathematical physics, together with the results obtained in functional analysis and boundary-value theory for equations with partial derivatives.
The Double Mellin Barnes Type Integrals And Their Application To Convolution Theory
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Author : Semyon B Yakubovich
language : en
Publisher: World Scientific
Release Date : 1992-05-26
The Double Mellin Barnes Type Integrals And Their Application To Convolution Theory written by Semyon B Yakubovich and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-26 with Mathematics categories.
This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.