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Linear Integral Operators
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Book Synopsis Linear Integral Equations by : Rainer Kress
Download or read book Linear Integral Equations written by Rainer Kress and published by Springer Science & Business Media. This book was released on 2013-12-04 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)
Book Synopsis Linear Integral Operators by : Konrad Jörgens
Download or read book Linear Integral Operators written by Konrad Jörgens and published by Pitman Advanced Publishing Program. This book was released on 1982 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bounded Integral Operators on L 2 Spaces by : P. R. Halmos
Download or read book Bounded Integral Operators on L 2 Spaces written by P. R. Halmos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something.
Book Synopsis Nonlinear Integral Operators and Applications by : Carlo Bardaro
Download or read book Nonlinear Integral Operators and Applications written by Carlo Bardaro and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications were soon extended beyond linear operators. In approximation theory, however, applications were limited to linear operators mainly by the fact that the notion of singularity of an integral operator was closely connected with its linearity. This book represents the first attempt at a comprehensive treatment of approximation theory by means of nonlinear integral operators in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed in order to obtain consistent approximation results. Applications to nonlinear summability, nonlinear integral equations and nonlinear sampling theory are given. In particular, the study of nonlinear sampling operators is important since the results permit the reconstruction of several classes of signals. In a wider context, the material of this book represents a starting point for new areas of research in nonlinear analysis. For this reason the text is written in a style accessible not only to researchers but to advanced students as well.
Book Synopsis Multilinear Operator Integrals by : Anna Skripka
Download or read book Multilinear Operator Integrals written by Anna Skripka and published by Springer Nature. This book was released on 2019-12-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive treatment of multilinear operator integral techniques. The exposition is structured to be suitable for a course on methods and applications of multilinear operator integrals and also as a research aid. The ideas and contributions to the field are surveyed and up-to-date results and methods are presented. Most practical constructions of multiple operator integrals are included along with fundamental technical results and major applications to smoothness properties of operator functions (Lipschitz and Hölder continuity, differentiability), approximation of operator functions, spectral shift functions, spectral flow in the setting of noncommutative geometry, quantum differentiability, and differentiability of noncommutative L^p-norms. Main ideas are demonstrated in simpler cases, while more involved, technical proofs are outlined and supplemented with references. Selected open problems in the field are also presented.
Book Synopsis Integral Operators in the Theory of Linear Partial Differential Equations by : Stefan Bergman
Download or read book Integral Operators in the Theory of Linear Partial Differential Equations written by Stefan Bergman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information.
Book Synopsis Integral Operators in Spaces of Summable Functions by : Mark Aleksandrovich Krasnoselʹskiĭ
Download or read book Integral Operators in Spaces of Summable Functions written by Mark Aleksandrovich Krasnoselʹskiĭ and published by . This book was released on 1976 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Operators in Non-Standard Function Spaces by : Vakhtang Kokilashvili
Download or read book Integral Operators in Non-Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-11 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Book Synopsis One-Dimensional Linear Singular Integral Equations by : I. Gohberg
Download or read book One-Dimensional Linear Singular Integral Equations written by I. Gohberg and published by Springer Science & Business Media. This book was released on 1992-01-01 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of linear one-dimensional singular integral equations. It is essentually a graduate textbook. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form. In this book material of the monograph [2] of the authors on one-dimensional singular integral operators is widely used. This monograph appeared in 1973 in Russian and later in German translation [3]. In the final text version the authors included many addenda and changes which have in essence changed character, structure and contents of the book and have, in our opinion, made it more suitable for a wider range of readers. Only the case of singular integral operators with continuous coefficients on a closed contour is considered herein. The case of discontinuous coefficients and more general contours will be considered in the second volume. We are grateful to the editor Professor G. Heinig of the volume and to the translators Dr. B. Luderer and Dr. S. Roch, and to G. Lillack, who did the typing of the manuscript, for the work they have done on this volume.
Book Synopsis Lectures on Gaussian Integral Operators and Classical Groups by : Yu. A. Neretin
Download or read book Lectures on Gaussian Integral Operators and Classical Groups written by Yu. A. Neretin and published by European Mathematical Society. This book was released on 2011 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators such as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. Prerequisites are standard university courses in linear algebra, functional analysis, and complex analysis.
Download or read book Linear Integral Operators written by and published by . This book was released on 1982* with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bounded and Compact Integral Operators by : David E. Edmunds
Download or read book Bounded and Compact Integral Operators written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).
Book Synopsis Partial Integral Operators and Integro-Differential Equations by : Jurgen Appell
Download or read book Partial Integral Operators and Integro-Differential Equations written by Jurgen Appell and published by CRC Press. This book was released on 2000-02-29 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.
Book Synopsis Linear Integral Operators by : Konrad Jorgens
Download or read book Linear Integral Operators written by Konrad Jorgens and published by . This book was released on 1970 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Solomon G. Mikhlin Publisher :Springer Science & Business Media ISBN 13 :9783540159674 Total Pages :530 pages Book Rating :4.1/5 (596 download)
Book Synopsis Singular Integral Operators by : Solomon G. Mikhlin
Download or read book Singular Integral Operators written by Solomon G. Mikhlin and published by Springer Science & Business Media. This book was released on 1987 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.
Book Synopsis Linear Integral Equations by : S.G. Mikhlin
Download or read book Linear Integral Equations written by S.G. Mikhlin and published by Courier Dover Publications. This book was released on 2020-10-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exploration of integral equations in several different contexts: Fredholm equations, Riesz-Schauder equations, symmetric integral equations and applications of integral equations in three-dimensional space, multi-dimensional spaces, vibrating membranes, more. 1960 edition.
Book Synopsis Basic Classes of Linear Operators by : Israel Gohberg
Download or read book Basic Classes of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.
