Aspects of the theory of bounded integral operators in L super p-spaces
Author: George O. Okikiolu
Publisher:
Published: 1971
Total Pages: 522
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: George O. Okikiolu
Publisher:
Published: 1971
Total Pages: 522
ISBN-13:
DOWNLOAD EBOOKAuthor: George Olatokunbo Okikiolu
Publisher:
Published: 1971
Total Pages: 522
ISBN-13:
DOWNLOAD EBOOKAuthor: G. O. Okikiolu
Publisher:
Published: 1971
Total Pages: 522
ISBN-13:
DOWNLOAD EBOOKAuthor: George O. Okikiolu
Publisher:
Published: 1971
Total Pages: 502
ISBN-13:
DOWNLOAD EBOOKAuthor: P. R. Halmos
Publisher: Springer
Published: 2011-11-15
Total Pages: 0
ISBN-13: 9783642670183
DOWNLOAD EBOOKThe 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: Paul Richard Halmos
Publisher:
Published: 1978
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKAuthor: M.A. Krasnosel'skii
Publisher: Springer
Published: 2011-11-08
Total Pages: 536
ISBN-13: 9789401015448
DOWNLOAD EBOOKThe 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: Viktor G. Kravchenko
Publisher: Springer
Published: 1994-05-31
Total Pages: 312
ISBN-13:
DOWNLOAD EBOOKThis book is devoted to the Fredholm theory of singular integral operators with shift in L p , 1 p This book is of interest to graduate students and mathematicians. The book is self-contained and can be used as a main reference for special course seminars on singular integral operators.
Author: Vakhtang Kokilashvili
Publisher: Birkhäuser
Published: 2016-05-11
Total Pages: 585
ISBN-13: 3319210157
DOWNLOAD EBOOKThis 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:
Publisher:
Published: 1978
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOK