Solution to a Singular Integro-Differential Equation III

In this paper we solve the singular integro-differential equation dy/dgt + (e(lambda ti) + e(mu ti)) Hy = e(nu ti) (i) in the space of semi-almost periodic distributions where A, it., ti are positive and rationally independent numbers and H is the Hilbert transform operator defined on the real line. Solution to the general problem dy/dt + a(t)Hy = f(t) (ii) when a(t), f (t) are any almost periodic functions still remains an open problem. It also remains an open problem to associate a physical problem with (i) and (ii). Nevertheless solutions to problems (i) and (ii) are important from the point of view of operator theory.