To questions of construction of integrated operators with осциллирующими in factors in space L2(Bn)

Abstract

To questions of construction of integrated operators with осциллирующими in factors in space L2(Bn)

A. G.Danekiants

Incoming article date: 30.10.2013

Article is devoted multidimensional integrated operators with homogeneous kernels and oscillating in factors of a special kind. The operators representing the sum of the composed are studied: the initial integrated operator with a homogeneous kernel, the operator with осциллирующим in factor and a homogeneous kernel. For the given operators the concept of a symbol, of which terms is defined the criterion neterovosti and the formula of calculation of an index is received. The task in view decision is based on a reduction of the multidimensional integrated equation to infinite diagonal system of the one-dimensional equations.

Keywords: Integral operators with homogeneous kernels,integral operators with oscillating factors, multidimensional integral equations