Some General Questions in the Theory of the Riemann Boundary Problem

In this paper we investigate the Riemann boundary problemΦ+(t) = G(t)Φ−(t) + g(t) for n pairs of functions. The solutions Φ± are to belong to the classes Ep±; the given function g belongs to the class Lp (1 < p < ∞). We enlarge the class of coefficients G for which the Noether theory remains valid. In the case n = 1, p = 2, necessary and sufficient conditions for Noetherianness are obtained. It is shown that the class of matrix-functions which admit factorization coincides with the class for which the Noether theory is valid. In the case n = 1 it is shown that one of the defect numbers is zero.