Some general questions in the theory of the Riemann boundary problem

In this paper we investigate the Riemann boundary problem
$$ \Phi^+(t)=G(t)\Phi^-(t)+g(t) $$
for $n$ pairs of functions. The solutions $\Phi^\pm$ are to belong to the classes $E_p^\pm$; the given function g belongs to the class $L_p$ $(1<p<\infty)$. 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.