Bounded And Compact Integral Operators
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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).
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.
Bounded Integral Operators On L2 Spaces
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Author : Paul Richard Halmos
language : en
Publisher: Springer
Release Date : 1978
Bounded Integral Operators On L2 Spaces written by Paul Richard Halmos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Collectively Compact Operator Approximation Theory And Applications To Integral Equations
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Author : Philip M. Anselone
language : en
Publisher: Prentice Hall
Release Date : 1971
Collectively Compact Operator Approximation Theory And Applications To Integral Equations written by Philip M. Anselone and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Linear Integral Operators
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Author : Konrad Jörgens
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1982
Linear Integral Operators written by Konrad Jörgens and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Mathematics categories.
Partial Integral Operators And Integro Differential Equations
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Author : Jurgen Appell
language : en
Publisher: CRC Press
Release Date : 2000-02-29
Partial Integral Operators And Integro Differential Equations written by Jurgen Appell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-29 with Mathematics categories.
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 linea
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 Spaces Of Summable Functions
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Author : Mark Aleksandrovich Krasnoselʹskiĭ
language : en
Publisher:
Release Date : 1976
Integral Operators In Spaces Of Summable Functions written by Mark Aleksandrovich Krasnoselʹskiĭ and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.
Kernels And Integral Operators For Continuous Sums Of Banach Spaces
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Author : Irwin E. Schochetman
language : en
Publisher: American Mathematical Soc.
Release Date : 1978
Kernels And Integral Operators For Continuous Sums Of Banach Spaces written by Irwin E. Schochetman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Banach spaces categories.
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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