Determination of singularities in an operator of partial radiation conditions

Abstract

The structure of an operator that determines the partial conditions of radiation in the scalar problem of diffraction theory is considered. Nonlocal boundary conditions are determined by a series setting a certain integro-differential operator. The principal part of this operator is presented in the explicit form of a hyper-singular operator and its components with lower-order singularities. The remaining rapidly converging part of the functional series determines an integral operator with a continuous kernel.