Image Normalization of Wiener-Hopf operators and boundary-transmission value problems for a junction of two half-planes

TL;DR

This paper applies image normalization techniques to Wiener-Hopf operators related to boundary-transmission problems in diffraction, addressing their solvability issues in mathematical physics contexts.

Contribution

It introduces an application of image normalization to analyze the solvability of Wiener-Hopf operators in boundary-transmission problems at a half-plane junction.

Findings

Normalization method clarifies operator solvability conditions

Different boundary conditions affect operator solvability

Application to diffraction problems in mathematical physics

Abstract

The present paper deals with an application of the image normalization technique for certain classes of Wiener-Hopf operators (WHOs) associated to ill-posed boundary-transmission value problems. We briefly describe the method of normalization and then apply it to boundary-transmission value problems issued from diffraction problems for a junction of two half-planes, which are relevant in mathematical physics applications. We consider different boundary-transmission conditions on the junction of the two semi-infinite half-planes and analyze the not normally solvability of the corresponding operators.