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
Multidimensional Singular Integrals And Integral Equations
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Author : S. G. Mikhlin
language : en
Publisher: Elsevier
Release Date : 2014-07-10
Multidimensional Singular Integrals And Integral Equations written by S. G. Mikhlin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.
Integral Transforms And Their Applications
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Author : Brian Davies
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integral Transforms And Their Applications written by Brian Davies 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.
This is a substantially updated, extended and reorganized third edition of an introductory text on the use of integral transforms. Chapter I is largely new, covering introductory aspects of complex variable theory. Emphasis is on the development of techniques and the connection between properties of transforms and the kind of problems for which they provide tools. Around 400 problems are accompanied in the text. It will be useful for graduate students and researchers working in mathematics and physics.
Integral Transforms Of Generalized Functions
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Author : Brychkov
language : en
Publisher: CRC Press
Release Date : 1989-04-20
Integral Transforms Of Generalized Functions written by 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 1989-04-20 with Mathematics categories.
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
Weighted Norm Inequalities For Integral Transforms With Product Kernals
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Author : Vakhtang Mikhaĭlovich Kokilashvili
language : en
Publisher:
Release Date : 2010
Weighted Norm Inequalities For Integral Transforms With Product Kernals written by Vakhtang Mikhaĭlovich Kokilashvili and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Inequalities (Mathematics) categories.
The book may be considered as a systematic and detailed analysis of a wide class of integral transforms with product kernels from the two-weighted boundedness point of view. The considered product kernels cover that case when factors of kernels have essential (less than one) singularities. The book intends to make a breakthrough in two directions: to cover multidimensional potentials, Hilbert transforms, strong maximal functions and at the same time, to present solutions of two-weighted problems for them which are much more complicated than one-weighted ones. In the given monograph two-weighted boundedness criteria for multiple Hardy transforms is reflected in the case when the two-dimensional weight on the right-hand side of an appropriate inequality is a product of two weight functions of single variable. In this case we present simpler and transparent criteria than those of E Sawyer for general weights. Moreover, we prove some new multidimensional Hardy{ type inequalities with general kernels. Weighted integral in-equalities for monotonic functions of several variables are also discussed. The main subjects of this book can be useful for applications both within various areas of the mathematical sciences (e.g. Fourier and Harmonic analysis, Fractional Calculus, BVP of PDE in Mathematical Physics, Stochastic Processes, Error Estimates in Numerical Analysis, etc.) as well as directly in some applied sciences.
Fractional Integral Transforms
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Author : Ahmed I. Zayed
language : en
Publisher: CRC Press
Release Date : 2024-03-28
Fractional Integral Transforms written by Ahmed I. Zayed and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-28 with Mathematics categories.
Fractional Integral Transforms: Theory and Applications presents over twenty-five integral transforms, many of which have never before been collected in one single volume. Some transforms are classic, such as Laplace, Fourier, etc, and some are relatively new, such as the Fractional Fourier, Gyrator, Linear Canonical, Special Affine Fourier Transforms, as well as, continuous Wavelet, Ridgelet, and Shearlet transforms. The book provides an overview of the theory of fractional integral transforms with examples of such transforms, before delving deeper into the study of important fractional transforms, including the fractional Fourier transform. Applications of fractional integral transforms in signal processing and optics are highlighted. The book’s format has been designed to make it easy for readers to extract the essential information they need to learn the about the fundamental properties of each transform. Supporting proofs and explanations are given throughout. Features Brings together integral transforms never before collected into a single volume A useful resource on fractional integral transforms for researchers and graduate students in mathematical analysis, applied mathematics, physics and engineering Written in an accessible style with detailed proofs and emphasis on providing the reader with an easy access to the essential properties of important fractional integral transforms Ahmed I. Zayed is a Professor of Mathematics at the Department of Mathematical Sciences, DePaul University, Chicago, and was the Chair of the department for 20 years, from 2001 until 2021. His research interests varied over the years starting with generalized functions and distributions to sampling theory, applied harmonic analysis, special functions and integral transforms. He has published two books and edited seven research monographs. He has written 22 book chapters, published 118 research articles, and reviewed 173 publications for the Mathematical Review and 81 for the Zentralblatt für Mathematik (zbMath). He has served on the Editorial Boards of 22 scientific research journals and has refereed over 200 research papers submitted to prestigious journals, among them are IEEE, SIAM, Amer. Math. Soc., Math Physics, and Optical Soc. Journals.
Index Transforms
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Author : S B Yakubovich
language : en
Publisher: World Scientific
Release Date : 1996-02-29
Index Transforms written by S 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. Contents:PreliminariesThe Kontorovich–Lebedev TransformThe Mehler–Fock TransformConvolution of the Kontorovich–Lebedev TransformGeneral Index TransformsIndex Transforms of the Lebedev–Skalskaya TypeIndex Tranforms with Hypergeometric Functions in the Kernel Readership: Researchers in mathematical analysis. keywords:Integral Transforms;Convolution;Fourier Transform;Mellin Transform;Kontorovich-Lebedev Transform;Index Transform;Hankel Transform;Mehler-Fock Transform;Olevskii Transform “It is a very well written book and the presentation of the material is commendable. In conclusion, it is useful book for research workers in the fields of integral transforms, special functions and fractional calculus.” Mathematics Abstracts “This is a well written book and it will be of interest not only to researchers but also to graduate students who are interested in the theory of integral transformations.” Mathematical Reviews “… This book presents a rather systematic and lucid account of the theory and applications of a fairly large variety of index transformations whose kernels involve not only the familiar Legendre and modified Bessel (or Macdonald) functions, but indeed also the Gaussian and other generalized hypergeometric functions, Meijer's G-function, and Foxs H-function. This state-of-the-art presentation of index transformations is recommended to all those graduate students and researchers (and other users of mathematics) who may find the various mathematical tools developed in this book to be potentially applicable in their works …” From the Foreword by H M Srivastava
Multidimensional Signals And Systems
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Author : Rudolf Rabenstein
language : en
Publisher: Springer Nature
Release Date : 2023-07-24
Multidimensional Signals And Systems written by Rudolf Rabenstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-24 with Computers categories.
This book covers the theory of multidimensional signals and systems and related practical aspects. It extends the properties and mathematical tools of one-dimensional signals and systems to multiple dimensions and covers relevant timeless topics including multidimensional transformations, multidimensional sampling as well as discrete multidimensional systems. A special emphasis is placed on physical systems described by partial differential equations, the construction of suitable integral transformations and the implementation of the corresponding discrete-time algorithms. To this end, signal spaces and functional transformations are introduced at a mathematical level provided by undergraduate programs in engineering and science. The presentation takes a comprehensive, illustrative and educational approach without reference to a particular application field. Instead, the book builds a solid theoretical concept of multidimensional signals and systems and shows the application to various problems relevant for practical scenarios.
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.
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.