Integral Operators in Spaces of Summable Functions

Krasnoselskii, M.A., P.P. Zabreiko, E.I. Pustylnik, and P.E. Sbolevskii

ISBN 10: 9028602941 / ISBN 13: 9789028602946

Published by Noordhoff International Publishing, 1976

About this Item

Hardcover; translated by T. Ando; surplus library copy with the usual stampings and reference number affixed to the spine; checkout sheet and bar code taped to front cover; bump to the upper front corner and a dark mark on the back bottom corner near spine; otherwise in good condition with clean text and tight binding.

Seller Inventory # 69932

Bibliographic Details

• Title: Integral Operators in Spaces of Summable Functions
• Publisher: Noordhoff International Publishing
• Publication Date: 1976
• Language: English
• ISBN 10: 9028602941
• ISBN 13: 9789028602946
• Binding: Hardcover
• Condition: UsedGood

About this title

Synopsis

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 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.

Language Notes

Text: Dutch, Russian (translation)