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

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. For each boundary-transmission value problem, we analyze the conditions under which the associated operator and the equivalent WHO are not normally solvable, and define the corresponding image normalized operators.