Geodesic
Some general questions in the theory of the Riemann boundary problem
Izvestiya. Mathematics , Tome 2 (1968) no. 5, pp. 1091-1099

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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 $L_p$ $(1$. 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. 
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     author = {I. B. Simonenko},
     title = {Some general questions in the theory of the {Riemann} boundary problem},
     journal = {Izvestiya. Mathematics },
     pages = {1091--1099},
     publisher = {mathdoc},
     volume = {2},
     number = {5},
     year = {1968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a8/}
}
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I. B. Simonenko. Some general questions in the theory of the Riemann boundary problem. Izvestiya. Mathematics , Tome 2 (1968) no. 5, pp. 1091-1099. http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a8/