Aspects of the Theory of Bounded Integral Operators in Lp-spaces
Author: George Olatokunbo Okikiolu
Publisher:
Published: 1971
Total Pages: 542
ISBN-13:
DOWNLOAD EBOOK →Author: George Olatokunbo Okikiolu
Publisher:
Published: 1971
Total Pages: 542
ISBN-13:
DOWNLOAD EBOOK →Author: P. R. Halmos
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 147
ISBN-13: 3642670164
DOWNLOAD EBOOK →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: George Olatokunbo Okikiolu
Publisher:
Published: 1971
Total Pages: 522
ISBN-13:
DOWNLOAD EBOOK →Author: Paul Richard Halmos
Publisher: Springer
Published: 1978
Total Pages: 160
ISBN-13:
DOWNLOAD EBOOK →Author: David E. Edmunds
Publisher: Springer Science & Business Media
Published: 2002-05-31
Total Pages: 664
ISBN-13: 9781402006197
DOWNLOAD EBOOK →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. It focuses on integral 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. We provide a list of problems which were open at the time of completion of the book. Audience: The book is aimed at a rather wide audience, ranging from researchers in functional and harmonic analysis to experts in applied mathematics and prospective students.
Author: Vakhtang Kokilashvili
Publisher: Birkhäuser
Published: 2016-05-11
Total Pages: 585
ISBN-13: 3319210157
DOWNLOAD EBOOK →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: Anupama Gupta
Publisher: LAP Lambert Academic Publishing
Published: 2012
Total Pages: 148
ISBN-13: 9783659288777
DOWNLOAD EBOOK →This book is a study of bounded weighted composite integral operators. The book is divided into five chapters and each chapter is further divided into several sections except the first chapter. The first chapter contains some introductory material. The composite integral operators are studied in the second chapter. The third chapter is devoted to a study of weighted composite integral operators. The linear and non-linear integral operator operators are reported in the fourth chapter. In the fifth chapter we characterize Frobenius-Perron operators between two Lp- spaces.