Theory And Applications Of Convolution Integral Equations

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Theory and Applications of Convolution Integral Equations

Author : Hari M. Srivastava
Publisher : Springer Science & Business Media
ISBN 13 : 9401580928
Total Pages : 259 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Theory and Applications of Convolution Integral Equations by : Hari M. Srivastava

Download or read book Theory and Applications of Convolution Integral Equations written by Hari M. Srivastava and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a state-of-the-art account of the theory and applications of integral equations of convolution type, and of certain classes of integro-differential and non-linear integral equations. An extensive and well-motivated discussion of some open questions and of various important directions for further research is also presented. The book has been written so as to be self-contained, and includes a list of symbols with their definitions. For users of convolution integral equations, the volume contains numerous, well-classified inversion tables which correspond to the various convolutions and intervals of integration. It also has an extensive, up-to-date bibliography. The convolution integral equations which are considered arise naturally from a large variety of physical situations and it is felt that the types of solutions discussed will be usefull in many diverse disciplines of applied mathematics and mathematical physical. For researchers and graduate students in the mathematical and physical sciences whose work involves the solution of integral equations.

The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory

Author : Nguyen Thanh Hai
Publisher : World Scientific
ISBN 13 : 9814506141
Total Pages : 308 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory by : Nguyen Thanh Hai

Download or read book The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory written by Nguyen Thanh Hai and published by World Scientific. This book was released on 1992-05-26 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:General H-Function of Two Variables and the Solution of its Convergence ProblemMain Properties, Series Presentations and Characteristic of the H-FunctionH-Function with the Third Characteristic and its Particular CasesG-Function of Two VariablesTable of Special Cases of the G-FunctionOne-Dimensional H-Transform in Spaces M-1(L) and M-1c,γ(L) and its Composition StructureClassical Laplace Convolution and its New PropertiesGeneral Integral Convolution for H-Function TransformExistence and Factorization Property of the ConvolutionNew Examples of Convolution for Classical Integral TransformsGeneralized Integral ConvolutionGeneral Leibniz Rules and Their Integral Analogs Readership: Researchers and students in mathematics, mechanics and physics. keywords:Mellin Transform of the One and Two Variables;Mellin-Barnes Integrals;Convolutions;Meijer's G-Function of Two Variables;Fox's H-Function of Two Variables;Fourier Transform;Laplace Transform;Gamma Function;Double Kampe de Feriet Hypergeometric Series;Leibniz Rules and Integral Analogs“The book gives a detailed and rigorous account of the theory of double Mellin-Barnes type integrals and contains new fundamental results and their applications to convolution theory. It is a valuable addition to the existing literature in the field of special functions and integral transforms.”K M Saksena “In the areas of special functions and integral transforms, teachers, researchers and graduate students are advised to refer to this work.” Siam Review

Volterra Integral Equations

Author : Hermann Brunner
Publisher : Cambridge University Press
ISBN 13 : 1316982653
Total Pages : 405 pages
Book Rating : 4.3/5 (169 download)

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Book Synopsis Volterra Integral Equations by : Hermann Brunner

Download or read book Volterra Integral Equations written by Hermann Brunner and published by Cambridge University Press. This book was released on 2017-01-20 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.

Integral Geometry and Convolution Equations

Author : V.V. Volchkov
Publisher : Springer Science & Business Media
ISBN 13 : 9401000239
Total Pages : 454 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Integral Geometry and Convolution Equations by : V.V. Volchkov

Download or read book Integral Geometry and Convolution Equations written by V.V. Volchkov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral geometry deals with the problem of determining functions by their integrals over given families of sets. These integrals de?ne the corresponding integraltransformandoneofthemainquestionsinintegralgeometryaskswhen this transform is injective. On the other hand, when we work with complex measures or forms, operators appear whose kernels are non-trivial but which describe important classes of functions. Most of the questions arising here relate, in one way or another, to the convolution equations. Some of the well known publications in this ?eld include the works by J. Radon, F. John, J. Delsarte, L. Zalcman, C. A. Berenstein, M. L. Agranovsky and recent monographs by L. H ̈ ormander and S. Helgason. Until recently research in this area was carried out mostly using the technique of the Fourier transform and corresponding methods of complex analysis. In recent years the present author has worked out an essentially di?erent methodology based on the description of various function spaces in terms of - pansions in special functions, which has enabled him to establish best possible results in several well known problems.

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.

Convolution Integral Equations, with Special Function Kernels

Author : H. M. Srivastava
Publisher : New York : Wiley
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis Convolution Integral Equations, with Special Function Kernels by : H. M. Srivastava

Download or read book Convolution Integral Equations, with Special Function Kernels written by H. M. Srivastava and published by New York : Wiley. This book was released on 1977 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Convolution Equations and Singular Integral Operators

Author : Leonid Lerer
Publisher : Springer Science & Business Media
ISBN 13 : 3764389567
Total Pages : 232 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Convolution Equations and Singular Integral Operators by : Leonid Lerer

Download or read book Convolution Equations and Singular Integral Operators written by Leonid Lerer and published by Springer Science & Business Media. This book was released on 2011-02-03 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of translations into English of several pioneering papers in the areas of discrete and continuous convolution operators and on the theory of singular integral operators published originally in Russian. The papers were wr- ten more than thirty years ago, but time showed their importance and growing in?uence in pure and applied mathematics and engineering. The book is divided into two parts. The ?rst ?ve papers, written by I. Gohberg and G. Heinig, form the ?rst part. They are related to the inversion of ?nite block Toeplitz matrices and their continuous analogs (direct and inverse problems) and the theory of discrete and continuous resultants. The second part consists of eight papers by I. Gohberg and N. Krupnik. They are devoted to the theory of one dimensional singular integral operators with discontinuous co- cients on various spaces. Special attention is paid to localization theory, structure of the symbol, and equations with shifts. ThisbookgivesanEnglishspeakingreaderauniqueopportunitytogetfam- iarized with groundbreaking work on the theory of Toepliz matrices and singular integral operators which by now have become classical. In the process of the preparation of the book the translator and the editors took care of several misprints and unessential misstatements. The editors would like to thank the translator A. Karlovich for the thorough job he has done. Our work on this book was started when Israel Gohberg was still alive. We see this book as our tribute to a great mathematician.

Spectral Theory of Approximation Methods for Convolution Equations

Author : Roland Hagen
Publisher : Birkhäuser
ISBN 13 : 3034890672
Total Pages : 388 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Spectral Theory of Approximation Methods for Convolution Equations by : Roland Hagen

Download or read book Spectral Theory of Approximation Methods for Convolution Equations written by Roland Hagen and published by Birkhäuser. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the present book is to propose a new algebraic approach to the study of norm stability of operator sequences which arise, for example, via discretization of singular integral equations on composed curves. A wide variety of discretization methods, including quadrature rules and spline or wavelet approximations, is covered and studied from a unique point of view. The approach takes advantage of the fruitful interplay between approximation theory, concrete operator theory, and local Banach algebra techniques. The book is addressed to a wide audience, in particular to mathematicians working in operator theory and Banach algebras as well as to applied mathematicians and engineers interested in theoretical foundations of various methods in general use, particularly splines and wavelets. The exposition contains numerous examples and exercises. Students will find a large number of suggestions for their own investigations.

Theory and Applications of Some New Classes of Integral Equations

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
ISBN 13 : 1461381126
Total Pages : 353 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Theory and Applications of Some New Classes of Integral Equations by : Alexander G. Ramm

Download or read book Theory and Applications of Some New Classes of Integral Equations written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for &tudents, research engineers, and mathematicians interested in applications or numerical analysis. Pure analysts will also find some new problems to tackle. Most of the material can be understood by a reader with a relatively modest knowledge of differential and inte gral equations and functional analysis. Readers interested in stochastic optimization will find a new theory of prac tical . importance. Readers interested in problems of static and quasi-static electrodynamics, wave scattering by small bodies of arbitrary shape, and corresponding applications in geophysics, optics, and radiophysics will find explicit analytical formulas for the scattering matrix, polarizability tensor, electrical capacitance of bodies of an arbitrary shape; numerical examples showing the practical utility of these formulas; two-sided variational estimates for the pol arizability tensor; and some open problems such as working out a standard program for calculating the capacitance and polarizability of bodies of arbitrary shape and numerical calculation of multiple integrals with weak singularities. Readers interested in nonlinear vibration theory will find a new method for qualitative study of stationary regimes in the general one-loop passive nonlinear network, including stabil ity in the large, convergence, and an iterative process for calculation the stationary regime. No assumptions concerning the smallness of the nonlinearity or the filter property of the linear one-port are made. New results in the theory of nonlinear operator equations form the basis for the study.

Basic Theory

Author : Anatoly Kochubei
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110571625
Total Pages : 489 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Basic Theory by : Anatoly Kochubei

Download or read book Basic Theory written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

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.

Index Transforms

Author : S B Yakubovich
Publisher : World Scientific
ISBN 13 : 9814500607
Total Pages : 264 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Index Transforms by : S B Yakubovich

Download or read book Index Transforms written by S B Yakubovich and published by World Scientific. This book was released on 1996-02-29 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Generalized Functions

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
ISBN 13 : 0817681744
Total Pages : 490 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Generalized Functions by : Ram P. Kanwal

Download or read book Generalized Functions written by Ram P. Kanwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises

The Hypergeometric Approach to Integral Transforms and Convolutions

Author : S. Semen B. Yakubovich
Publisher : Kluwer Academic Pub
ISBN 13 : 9780792328568
Total Pages : 324 pages
Book Rating : 4.3/5 (285 download)

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Book Synopsis The Hypergeometric Approach to Integral Transforms and Convolutions by : S. Semen B. Yakubovich

Download or read book The Hypergeometric Approach to Integral Transforms and Convolutions written by S. Semen B. Yakubovich and published by Kluwer Academic Pub. This book was released on 1994 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the theory and applications of integral transforms and convolutions of certain classes of integral, integrodifferential equations, and operational calculus. An extensive discussion is presented, based on the universal hypergeometric approach, i.e. many constructions of convolution and integral transforms are obtained using the theory of Mellin--Barnes integrals and the Mellin transforms of hypergeometric type functions. This approach is spread on so-called index transforms, in which the Kontorovich--Lebedev and the Mehler--Fock transforms play a very important part. The general constructions of index transforms are given and application to the evaluation of improper integral with respect to a parameter of special function (index) is considered. The operational calculus for general integrodifferential operators is constructed for both new types of convolutions. 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 graduate students in the mathematical and physical sciences whose work involves integral transforms and convolutions.

Index Transforms

Author : Semen B. Yakubovich
Publisher : World Scientific
ISBN 13 : 9789810222161
Total Pages : 272 pages
Book Rating : 4.2/5 (221 download)

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Book Synopsis Index Transforms by : Semen B. Yakubovich

Download or read book Index Transforms written by Semen B. Yakubovich and published by World Scientific. This book was released on 1996 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 p 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.

Random Integral Equations with Applications to Stochastic Systems

Author : C. P. Tsokos
Publisher : Springer
ISBN 13 : 3540369929
Total Pages : 181 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Random Integral Equations with Applications to Stochastic Systems by : C. P. Tsokos

Download or read book Random Integral Equations with Applications to Stochastic Systems written by C. P. Tsokos and published by Springer. This book was released on 2006-11-15 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors have two main objectives in these notes. First, they wish to give a complete presentation of the theory of existence and uniqueness of random solutions of the most general random Volterra and Fredholm equations which have been studied heretofore. Second, to emphasize the application of their theory to stochastic systems which have not been extensively studied before due to mathematical difficulties that arise. These notes will be of value to mathematicians, probabilists, and engineers who are working in the area of systems theory or to those who are interested in the theory of random equations.

Representation of Lie Groups and Special Functions

Author : N.Ja. Vilenkin
Publisher : Springer Science & Business Media
ISBN 13 : 9401728852
Total Pages : 518 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Representation of Lie Groups and Special Functions by : N.Ja. Vilenkin

Download or read book Representation of Lie Groups and Special Functions written by N.Ja. Vilenkin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1991-1993 our three-volume book "Representation of Lie Groups and Spe cial Functions" was published. When we started to write that book (in 1983), editors of "Kluwer Academic Publishers" expressed their wish for the book to be of encyclopaedic type on the subject. Interrelations between representations of Lie groups and special functions are very wide. This width can be explained by existence of different types of Lie groups and by richness of the theory of their rep resentations. This is why the book, mentioned above, spread to three big volumes. Influence of representations of Lie groups and Lie algebras upon the theory of special functions is lasting. This theory is developing further and methods of the representation theory are of great importance in this development. When the book "Representation of Lie Groups and Special Functions" ,vol. 1-3, was under preparation, new directions of the theory of special functions, connected with group representations, appeared. New important results were discovered in the traditional directions. This impelled us to write a continuation of our three-volume book on relationship between representations and special functions. The result of our further work is the present book. The three-volume book, published before, was devoted mainly to studying classical special functions and orthogonal polynomials by means of matrix elements, Clebsch-Gordan and Racah coefficients of group representations and to generaliza tions of classical special functions that were dictated by matrix elements of repre sentations.