We consider a problem of wave diffraction characterized with higher order boundary conditions. From the mathematical point of view, the problem is formulated as a boundary-transmission problem for the Helmholtz equation within a Bessel potential space framework. Operator theoretical methods are used to deal with this problem and, as a consequence, several convolution type operators are constructed and associated to the problem.
A Fredholm characterization of these operators is obtained for certain smoothness space orders, and a consequent mathematical analysis of the initial problem is derived.