Integrals And Operators
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Integrals And Operators
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Author : I.E. Segal
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrals And Operators written by I.E. Segal 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.
TO THE SECOND EDITION Since publication of the First Edition several excellent treatments of advanced topics in analysis have appeared. However, the concentration and penetration of these treatises naturally require much in the way of technical preliminaries and new terminology and notation. There consequently remains a need for an introduction to some of these topics which would mesh with the material of the First Edition. Such an introduction could serve to exemplify the material further, while using it to shorten and simplify its presentation. It seemed particularly important as well as practical to treat briefly but cogently some of the central parts of operator algebra and higher operator theory, as these are presently represented in book form only with a degree of specialization rather beyond the immediate needs or interests of many readers. Semigroup and perturbation theory provide connections with the theory of partial differential equations. C*-algebras are important in har monic analysis and the mathematical foundations of quantum mechanics. W*-algebras (or von Neumann rings) provide an approach to the theory of multiplicity of the spectrum and some simple but key elements of the gram mar of analysis, of use in group representation theory and elsewhere. The v vi Preface to the Second Edition theory of the trace for operators on Hilbert space is both important in itself and a natural extension of earlier integration-theoretic ideas.
Bounded Integral Operators On L 2 Spaces
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Author : P. R. Halmos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Bounded Integral Operators On L 2 Spaces written by P. R. Halmos 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 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.
Lectures On Gaussian Integral Operators And Classical Groups
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Author : Yu. A. Neretin
language : en
Publisher: European Mathematical Society
Release Date : 2011
Lectures On Gaussian Integral Operators And Classical Groups written by Yu. A. Neretin and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Geometry, Differential categories.
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.
Bounded And Compact Integral Operators
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Author : David E. Edmunds
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Bounded And Compact Integral Operators written by David E. Edmunds 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 2013-06-29 with Mathematics categories.
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).
Integral Operators In The Theory Of Linear Partial Differential Equations
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Author : Stefan Bergman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integral Operators In The Theory Of Linear Partial Differential Equations written by Stefan Bergman 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 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.
Singular Integral Operators
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Author : Solomon G. Mikhlin
language : en
Publisher: Springer Science & Business Media
Release Date : 1987
Singular Integral Operators written by Solomon G. Mikhlin 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 1987 with Mathematics categories.
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.
Integral Operators In Non Standard Function Spaces
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Author : Vakhtang Kokilashvili
language : en
Publisher: Birkhäuser
Release Date : 2016-05-11
Integral Operators In Non Standard Function Spaces written by Vakhtang Kokilashvili and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-11 with Mathematics categories.
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.
Nonlinear Integral Operators And Applications
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Author : Carlo Bardaro
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22
Nonlinear Integral Operators And Applications written by Carlo Bardaro and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.
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.
Systems Approximation Singular Integral Operators And Related Topics
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Author : Alexander A. Borichev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Systems Approximation Singular Integral Operators And Related Topics written by Alexander A. Borichev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.
Singular Integral Operators
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Author : S. G. Mikhlin
language : de
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1986-12-31
Singular Integral Operators written by S. G. Mikhlin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-12-31 with Mathematics categories.
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