Integral Equations With Difference Kernels On Finite Intervals

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Integral Equations with Difference Kernels on Finite Intervals

Author : Lev A. Sakhnovich
Publisher : Birkhäuser
ISBN 13 : 3319164899
Total Pages : 240 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Integral Equations with Difference Kernels on Finite Intervals by : Lev A. Sakhnovich

Download or read book Integral Equations with Difference Kernels on Finite Intervals written by Lev A. Sakhnovich and published by Birkhäuser. This book was released on 2015-05-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on solving integral equations with difference kernels on finite intervals. The corresponding problem on the semiaxis was previously solved by N. Wiener–E. Hopf and by M.G. Krein. The problem on finite intervals, though significantly more difficult, may be solved using our method of operator identities. This method is also actively employed in inverse spectral problems, operator factorization and nonlinear integral equations. Applications of the obtained results to optimal synthesis, light scattering, diffraction, and hydrodynamics problems are discussed in this book, which also describes how the theory of operators with difference kernels is applied to stable processes and used to solve the famous M. Kac problems on stable processes. In this second edition these results are extensively generalized and include the case of all Levy processes. We present the convolution expression for the well-known Ito formula of the generator operator, a convolution expression that has proven to be fruitful. Furthermore we have added a new chapter on triangular representation, which is closely connected with previous results and includes a new important class of operators with non-trivial invariant subspaces. Numerous formulations and proofs have now been improved, and the bibliography has been updated to reflect more recent additions to the body of literature.

Integral Equations with Difference Kernels on Finite Intervals

Author : Lev A Sakhnovich
Publisher :
ISBN 13 : 9783034889872
Total Pages : 188 pages
Book Rating : 4.8/5 (898 download)

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Book Synopsis Integral Equations with Difference Kernels on Finite Intervals by : Lev A Sakhnovich

Download or read book Integral Equations with Difference Kernels on Finite Intervals written by Lev A Sakhnovich and published by . This book was released on 1995-01-26 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Integral Equations

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 0203881052
Total Pages : 1143 pages
Book Rating : 4.2/5 (38 download)

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Book Synopsis Handbook of Integral Equations by : Andrei D. Polyanin

Download or read book Handbook of Integral Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2008-02-12 with total page 1143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa

Infinite Interval Problems for Differential, Difference and Integral Equations

Author : R.P. Agarwal
Publisher : Springer Science & Business Media
ISBN 13 : 9401007187
Total Pages : 350 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Infinite Interval Problems for Differential, Difference and Integral Equations by : R.P. Agarwal

Download or read book Infinite Interval Problems for Differential, Difference and Integral Equations written by R.P. Agarwal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite interval problems abound in nature and yet until now there has been no book dealing with such problems. The main reason for this seems to be that until the 1970's for the infinite interval problem all the theoretical results available required rather technical hypotheses and were applicable only to narrowly defined classes of problems. Thus scientists mainly offer~d and used special devices to construct the numerical solution assuming tacitly the existence of a solution. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study the existence of solutions to infinite interval problems. This has resulted in widely applicable results. This monograph is a cumulation mainly of the authors' research over a period of more than ten years and offers easily verifiable existence criteria for differential, difference and integral equations over the infinite interval. An important feature of this monograph is that we illustrate almost all the results with examples. The plan of this monograph is as follows. In Chapter 1 we present the existence theory for second order boundary value problems on infinite intervals. We begin with several examples which model real world phenom ena. A brief history of the infinite interval problem is also included. We then present general existence results for several different types of boundary value problems. Here we note that for the infinite interval problem only two major approaches are available in the literature.

Handbook of Mathematics for Engineers and Scientists

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1420010514
Total Pages : 1542 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Mathematics for Engineers and Scientists by : Andrei D. Polyanin

Download or read book Handbook of Mathematics for Engineers and Scientists written by Andrei D. Polyanin and published by CRC Press. This book was released on 2006-11-27 with total page 1542 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.

U.S. Government Research Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 1310 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis U.S. Government Research Reports by :

Download or read book U.S. Government Research Reports written by and published by . This book was released on 1964 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Inverse Problems and Nonlinear Evolution Equations

Author : Alexander L. Sakhnovich
Publisher : Walter de Gruyter
ISBN 13 : 3110258617
Total Pages : 356 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Inverse Problems and Nonlinear Evolution Equations by : Alexander L. Sakhnovich

Download or read book Inverse Problems and Nonlinear Evolution Equations written by Alexander L. Sakhnovich and published by Walter de Gruyter. This book was released on 2013-07-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund–Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses.

Integral Methods in Science and Engineering

Author : Christian Constanda
Publisher : Springer
ISBN 13 : 3030160777
Total Pages : 478 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Integral Methods in Science and Engineering by : Christian Constanda

Download or read book Integral Methods in Science and Engineering written by Christian Constanda and published by Springer. This book was released on 2019-07-18 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include: Asymptotic analysis Boundary-domain integral equations Viscoplastic fluid flow Stationary waves Interior Neumann shape optimization Self-configuring neural networks This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

Modern Methods in Mathematical Physics

Author : Vladimir Ryzhov
Publisher : Springer Nature
ISBN 13 : 9811949158
Total Pages : 201 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Modern Methods in Mathematical Physics by : Vladimir Ryzhov

Download or read book Modern Methods in Mathematical Physics written by Vladimir Ryzhov and published by Springer Nature. This book was released on 2022-11-03 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides ideas for implementing Wolfram Mathematica to solve linear integral equations. The book introduces necessary theoretical information about exact and numerical methods of solving integral equations. Every method is supplied with a large number of detailed solutions in Wolfram Mathematica. In addition, the book includes tasks for individual study. This book is a supplement for students studying “Integral Equations”. In addition, the structure of the book with individual assignments allows to use it as a base for various courses.

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1970 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3034889089
Total Pages : 244 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces by : Daniel Alpay

Download or read book Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproducing kernel Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.

IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity

$Download IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity PDF Online Free$

Author : I. David Abrahams
Publisher : Springer Science & Business Media
ISBN 13 : 9401700877
Total Pages : 355 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity by : I. David Abrahams

Download or read book IUTAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity written by I. David Abrahams and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Conference Proceedings are intended to summarise the latest developments in diffraction and scattering theory as reported at the IU TAM Symposium on Diffraction and Scattering in Fluid Mechanics and Elasticity held in Manchester, England on 16-20 July 2000. This in formal meeting was organised to discuss mathematical advances, both from the theoretical and more applied points of view. However, its pri mary goal was to bring together groups of researchers working in dis parate application areas, but who nevertheless share common models, phenomenological features arising in such problems, and common math ematical tools. To this end, we were delighted to have four Plenary Speakers, Professors Allan Pierce, Ed Kerschen, Roger Grimshaw and John Willis FRS, who are undisputed leaders in the four thematic ar eas of our meeting (these are respectively acoustics, aeroacoustics, water or other free surface waves, elasticity). These Proceedings should offer an excellent vehicle for continuing the dialogue between these groups of researchers. The participants were invited because of their expertise and recent contributions to this field. Collectively, there were around 90 contrib utors to the Symposium from some 13 countries located all around the world. These included 45 speakers, 35 co-authors and about 10 other delegates. Individuals came from many of the major international cen tres of excellence in the field of scattering theory.

Computational Methods for Linear Integral Equations

Author : Prem Kythe
Publisher : Springer Science & Business Media
ISBN 13 : 1461201012
Total Pages : 525 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Computational Methods for Linear Integral Equations by : Prem Kythe

Download or read book Computational Methods for Linear Integral Equations written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

New Results in Operator Theory and Its Applications

Author : Israel Gohberg
Publisher : Birkhäuser
ISBN 13 : 3034889100
Total Pages : 269 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis New Results in Operator Theory and Its Applications by : Israel Gohberg

Download or read book New Results in Operator Theory and Its Applications written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Israel Glazman, an outstanding personality and distinguished mathematician, the author of many remarkable papers and books in operator theory and its applications. The present book opens with an essay devoted to Glazman's life and scientific achievements. It focusses on the areas of his unusually wide interests and consists of 18 mathematical papers in spectral theory of differential operators and linear operators in Hilbert and Banach spaces, analytic operator functions, ordinary and partial differential equations, functional equations, mathematical physics, nonlinear functional analysis, approximation theory and optimization, and mathematical statistics. The book gives a picture of the current state of some important problems in areas of operator theory and its applications and will be of interest to a wide group of researchers working in pure and applied mathematics.

Measures of Noncompactness in Metric Fixed Point Theory

Author : José María Ayerbe Toledano
Publisher : Springer Science & Business Media
ISBN 13 : 9783764357948
Total Pages : 234 pages
Book Rating : 4.3/5 (579 download)

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Book Synopsis Measures of Noncompactness in Metric Fixed Point Theory by : José María Ayerbe Toledano

Download or read book Measures of Noncompactness in Metric Fixed Point Theory written by José María Ayerbe Toledano and published by Springer Science & Business Media. This book was released on 1997 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to metric fixed point theory. The goal is to develop, in a self-contained fashion, those results in this theory which involve the use of measures of noncompactness. Some of the well-known fixed point theorems are included with several applications to the theory of differential equations. This book is mainly addressed to graduate students who wish to learn about metric fixed point theory, but it will also be useful to researchers in the area. Most of the results presented here were obtained by the authors over the last ten years and have not previously appeared in any other textbook.

Recent Advances in Operator Theory and Its Applications

Author : Marinus A. Kaashoek
Publisher : Springer Science & Business Media
ISBN 13 : 3764373989
Total Pages : 478 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Recent Advances in Operator Theory and Its Applications by : Marinus A. Kaashoek

Download or read book Recent Advances in Operator Theory and Its Applications written by Marinus A. Kaashoek and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a selection of carefully refereed research papers, most of which were presented at the fourteenth International Workshop on Operator Theory and its Applications (IWOTA), held at Cagliari, Italy, from June 24-27, 2003. The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.

Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations

Author : M. Sh Birman
Publisher : American Mathematical Soc.
ISBN 13 : 9780821841068
Total Pages : 218 pages
Book Rating : 4.8/5 (41 download)

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Book Synopsis Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations by : M. Sh Birman

Download or read book Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations written by M. Sh Birman and published by American Mathematical Soc.. This book was released on 1991 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Leningrad Seminar on mathematical physics, begun in 1947 by V. I. Smirnov and now run by O. A. Ladyzhenskaya, is sponsored by Leningrad University and the Leningrad Branch of the Steklov Mathematical Institute of the Academy of Sciences of the USSR. The main topics of the seminar center on the theory of boundary value problems and related questions of analysis and mathematical physics. This volume contains adaptations of lectures presented at the seminar during the academic year 1989-1990. For the most part, the papers are devoted to investigations of the spectrum of the Schrödinger operator (or its generalizations) perturbed by some relatively compact operator. The book studies the discrete spectrum that emerges in the spectral gaps of the nonperturbed operator, and considers the corresponding estimates and asymptotic formulas for spectrum distribution functions in the large-coupling-constant limit. The starting point here is the opening paper, which is devoted to the important case of a semi-infinite gap. The book also covers the case of inner gaps, related questions in the theory of functions, and an integral equation with difference kernel on a finite interval. The collection concludes with a paper focusing on the classical problem of constructing scattering theory for the Schrödinger operator with potential decreasing faster than the Coulomb potential