Integral Operators In Spaces Of Summable Functions

Author : M.A. Krasnosel'skii,P.P. Zabreyko,E.I. Pustylnik,P.E. Sobolevski
Publisher : Springer
Page : 536 pages
File Size : 48,7 Mb
Release : 2011-11-08
Category : Mathematics
ISBN : 9401015449

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Integral operators in spaces of summable functions by M.A. Krasnosel'skii,P.P. Zabreyko,E.I. Pustylnik,P.E. Sobolevski Pdf

The investigation of many mathematical problems is significantly simplified if it is possible to reduce them to equations involving continuous or com pletely continuous operators in function spaces. In particular, this is true for non-linear boundary value problems and for integro-differential and integral equations. To effect a transformation to equations with continuous or completely continuous operators, it is usually necessary to reduce the original problem to one involving integral equations. Here, negative and fractional powers of those unbounded differential operators which constitute 'principal parts' of the original problem, are used in an essential way. Next there is chosen or constructed a function space in which the corresponding integral oper ator possesses sufficiently good properties. Once such a space is found, the original problem can often be analyzed by applying general theorems (Fredholm theorems in the study of linear equations, fixed point principles in the study of non-linear equations, methods of the theory of cones in the study of positive solutions, etc.). In other words, the investigation of many problems is effectively divided into three independent parts: transformation to an integral equation, investi gation of the corresponding integral expression as an operator acting in function spaces, and, finally, application of general methods of functional analysis to the investigation of the linear and non-linear equations.

Author : M.A. Krasnosel'skii,P.P. Zabreyko,E.I. Pustylnik,P.E. Sobolevski
Publisher : Springer
Page : 0 pages
File Size : 44,5 Mb
Release : 2014-01-14
Category : Mathematics
ISBN : 9401015422

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Integral operators in spaces of summable functions by M.A. Krasnosel'skii,P.P. Zabreyko,E.I. Pustylnik,P.E. Sobolevski Pdf

The investigation of many mathematical problems is significantly simplified if it is possible to reduce them to equations involving continuous or com pletely continuous operators in function spaces. In particular, this is true for non-linear boundary value problems and for integro-differential and integral equations. To effect a transformation to equations with continuous or completely continuous operators, it is usually necessary to reduce the original problem to one involving integral equations. Here, negative and fractional powers of those unbounded differential operators which constitute 'principal parts' of the original problem, are used in an essential way. Next there is chosen or constructed a function space in which the corresponding integral oper ator possesses sufficiently good properties. Once such a space is found, the original problem can often be analyzed by applying general theorems (Fredholm theorems in the study of linear equations, fixed point principles in the study of non-linear equations, methods of the theory of cones in the study of positive solutions, etc.). In other words, the investigation of many problems is effectively divided into three independent parts: transformation to an integral equation, investi gation of the corresponding integral expression as an operator acting in function spaces, and, finally, application of general methods of functional analysis to the investigation of the linear and non-linear equations.

Author : Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko
Publisher : Birkhäuser
Page : 567 pages
File Size : 55,6 Mb
Release : 2016-05-11
Category : Mathematics
ISBN : 9783319210155

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Integral Operators in Non-Standard Function Spaces by Vakhtang Kokilashvili,Alexander Meskhi,Humberto Rafeiro,Stefan Samko Pdf

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.

Author : Mark Aleksandrovich Krasnoselʹskiĭ
Publisher : Unknown
Page : 544 pages
File Size : 41,6 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015049299624

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Integral Operators in Spaces of Summable Functions by Mark Aleksandrovich Krasnoselʹskiĭ Pdf

Author : P. R. Halmos,V. S. Sunder
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642670169

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Bounded Integral Operators on L 2 Spaces by P. R. Halmos,V. S. Sunder Pdf

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.

Author : S. Okada,Werner J. Ricker,Enrique A. Sánchez Pérez
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 41,8 Mb
Release : 2008-09-09
Category : Mathematics
ISBN : 9783764386481

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Optimal Domain and Integral Extension of Operators by S. Okada,Werner J. Ricker,Enrique A. Sánchez Pérez Pdf

This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Most of the material appears in print for the first time. The book has an interdisciplinary character and is aimed at graduates, postgraduates, and researchers in modern operator theory.

Author : Jurgen Appell,Anatolij Kalitvin,Petr Zabrejko
Publisher : CRC Press
Page : 579 pages
File Size : 45,9 Mb
Release : 2000-02-29
Category : Mathematics
ISBN : 9781482270402

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Partial Integral Operators and Integro-Differential Equations by Jurgen Appell,Anatolij Kalitvin,Petr Zabrejko Pdf

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

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 48,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400959880

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : M. Hazewinkel
Publisher : Springer
Page : 952 pages
File Size : 41,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489937933

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Encyclopaedia of Mathematics by M. Hazewinkel Pdf

Author : Semën Samsonovich Kutateladze
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400901957

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Vector Lattices and Intergal Operators by Semën Samsonovich Kutateladze Pdf

The theory of vector lattices, stemming from the mid-thirties, is now at the stage where its main achievements are being summarized. The sweeping changes of the last two decades have changed its image completely. The range of its application was expanded and enriched so as to embrace diverse branches of the theory of functions, geometry of Banach spaces, operator theory, convex analysis, etc. Furthermore, the theory of vector lattices was impregnated with principally new tools and techniques from other sections of mathematics. These circumstances gave rise to a series of mono graphs treating separate aspects of the theory and oriented to specialists. At the same time, the necessity of a book intended for a wider readership, reflecting the modern diretions of research became clear. The present book is meant to be an attempt at implementing this task. Although oriented to readers making their first acquaintance with vector-lattice theory, it is composed so that the main topics dealt with in the book reach the current level of research in the field, which is of interest and import for specialists. The monograph was conceived so as to be divisible into two parts that can be read independently of one another. The first part is mainly Chapter 1, devoted to the so-called Boolean-valued analysis of vector lattices. The term designates the applica tion of the theory of Boolean-valued models by D. Scott, R. Solovay and P.

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 421 pages
File Size : 55,5 Mb
Release : 2020-04-02
Category : Mathematics
ISBN : 9781108715744

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Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Author : David E. Edmunds,V.M Kokilashvili,Alexander Meskhi
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 53,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599221

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Bounded and Compact Integral Operators by David E. Edmunds,V.M Kokilashvili,Alexander Meskhi Pdf

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).

Author : Stefan Samko
Publisher : CRC Press
Page : 378 pages
File Size : 52,9 Mb
Release : 2001-10-25
Category : Mathematics
ISBN : 9781482264968

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Hypersingular Integrals and Their Applications by Stefan Samko Pdf

Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before

Author : Sergey V. Astashkin
Publisher : Springer Nature
Page : 567 pages
File Size : 45,7 Mb
Release : 2020-07-27
Category : Mathematics
ISBN : 9783030478902

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The Rademacher System in Function Spaces by Sergey V. Astashkin Pdf

This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in Lp-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces.

Author : S. G. Krein,E. M. Semenov
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 45,8 Mb
Release : 2002-10-21
Category : Mathematics
ISBN : 9780821831762

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Interpolation of Linear Operators by S. G. Krein,E. M. Semenov Pdf