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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1968_2_5_a8,
     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/}
}
TY  - JOUR
AU  - I. B. Simonenko
TI  - Some general questions in the theory of the Riemann boundary problem
JO  - Izvestiya. Mathematics 
PY  - 1968
SP  - 1091
EP  - 1099
VL  - 2
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a8/
LA  - en
ID  - IM2_1968_2_5_a8
ER  - 
%0 Journal Article
%A I. B. Simonenko
%T Some general questions in the theory of the Riemann boundary problem
%J Izvestiya. Mathematics 
%D 1968
%P 1091-1099
%V 2
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1968_2_5_a8/
%G en
%F IM2_1968_2_5_a8
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/

[1] Simonenko I. B., “Kraevaya zadacha Rimana s izmerimym koeffitsientom”, Dokl. AN SSSR, 135:3 (1960), 538–541 | MR | Zbl

[2] Simonenko I. B., “Kraevaya zadacha Rimana dlya $n$ par funktsii s izmerimymi koeffitsientami i ee primenenie k issledovaniyu singulyarnykh integralov v prostranstvakh $L_p$ s vesami”, Dokl. AN SSSR, 141:1 (1961), 36–39 | MR | Zbl

[3] Simonenko I. B., “Kraevaya zadacha Rimana dlya $n$ par funktsii s izmerimymi koeffitsientami i ee primenenie k issledovaniyu singulyarnykh integralov v prostranstvakh $L_p$ s vesami”, Izv. AN SSSR. Ser. matem., 28 (1964), 277–306 | MR | Zbl

[4] Simonenko I. B., “Novyi obschii metod issledovaniya lineinykh operatornykh uravnenii tipa singulyarnykh integralnykh uravnenii”, Dokl. AN SSSR, 158:4 (1964), 790–793 | MR | Zbl

[5] Simonenko I. B., “Novyi obschii metod issledovaniya lineinykh operatornykh uravnenii tipa singulyarnykh integralnykh uravnenii. I”, Izv. AN SSSR. Ser. matem., 29 (1965), 567–586 | MR | Zbl

[6] Simonenko I. B., “Lokalnyi printsip v kraevoi zadache Rimana”, Soobscheniya na 1-i konferentsii Rostovskogo matem. ob-va, Rostov-na-Donu, 1967

[7] Gokhberg I. Ts., “O chisle reshenii odnorodnogo singulyarnogo integralnogo uravneniya s nepreryvnymi koeffitsientami”, Dokl. AN SSSR, 122:3 (1958), 327–330 | Zbl

[8] Mikhlin S. G., “Singulyarnye integralnye uravneniya s nepreryvnymi koeffitsientami”, Dokl. AN SSSR, 59:3 (1948), 435–438

[9] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M., 1950

[10] Devinatz Allen, “Toeplits operators on $H_2$ space”, Trans. Amer. Hath. Soc., 112:2 (1964), 304–317 | DOI | MR | Zbl