Geodesic
To the Solution of the Hilbert Problem with Infinite Index
Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 724-734 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we obtain a generalization of the method of regularizing multipliers for the solution of the Hilbert boundary-value problem with finite index in the theory of analytic functions to the case of an infinite power-behaved index. This method is used to obtain a general solution of the homogeneous Hilbert problem for the half-plane, a solution that depends on the existence and the number of entire functions possessing mirror symmetry with respect to the real axis and satisfying some additional constraints related to the singularity characteristic of the index. To solve of the inhomogeneous problem, we essentially use a specially constructed solution of the homogeneous problem whereby we reduce the boundary condition of the Hilbert problem to a Dirichlet problem. 
@article{MZM_2003_73_5_a8,
     author = {R. B. Salimov and P. L. Shabalin},
     title = {To the {Solution} of the {Hilbert} {Problem} with {Infinite} {Index}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {724--734},
     year = {2003},
     volume = {73},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a8/}
}
TY  - JOUR
AU  - R. B. Salimov
AU  - P. L. Shabalin
TI  - To the Solution of the Hilbert Problem with Infinite Index
JO  - Matematičeskie zametki
PY  - 2003
SP  - 724
EP  - 734
VL  - 73
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a8/
LA  - ru
ID  - MZM_2003_73_5_a8
ER  - 
%0 Journal Article
%A R. B. Salimov
%A P. L. Shabalin
%T To the Solution of the Hilbert Problem with Infinite Index
%J Matematičeskie zametki
%D 2003
%P 724-734
%V 73
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a8/
%G ru
%F MZM_2003_73_5_a8
R. B. Salimov; P. L. Shabalin. To the Solution of the Hilbert Problem with Infinite Index. Matematičeskie zametki, Tome 73 (2003) no. 5, pp. 724-734. http://geodesic.mathdoc.fr/item/MZM_2003_73_5_a8/

[1] Sandrygailo I. E., “O kraevoi zadache Gilberta s beskonechnym indeksom dlya poluploskosti”, Izv. AN BSSR. Ser. fiz.-matem. nauk, 1974, no. 6, 16–23 | MR | Zbl

[2] Alekna P. Yu., “Kraevaya zadacha Gilberta s beskonechnym indeksom logarifmicheskogo poryadka dlya poluploskosti”, Lit. matem. sb., 1977, no. 1, 5–12 | MR | Zbl

[3] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968

[4] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977

[5] Chibrikova L. I., Osnovnye granichnye zadachi dlya analiticheskikh funktsii, Izd-vo Kazanskogo un-ta, Kazan, 1977

[6] Chibrikova L. I., Salekhov L. G., “K resheniyu kraevoi zadachi Gilberta”, Trudy seminara po kraevym zadacham, 8, Izd-vo Kazanskogo un-ta, Kazan, 1971, 155–175

[7] Salimov R. B., Seleznev V. V., “K resheniyu kraevoi zadachi Gilberta s razryvnymi koeffitsientami”, Trudy seminara po kraevym zadacham, 16, Izd-vo Kazanskogo un-ta, Kazan, 1979, 149–162 | MR

[8] Govorov N. V., Kraevaya zadacha Rimana s beskonechnym indeksom, Nauka, M., 1986 | Zbl

[9] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[10] Markushevich A. I., Teoriya analiticheskikh funktsii, T. 2, Nauka, M., 1968