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. 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.