Geodesic
A homogeneous Hilbert problem with discontinuous coefficients and two-side curling at infinity of order~$1/2\leq\rho1$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2012), pp. 67-71.

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

We study a homogeneous Riemann–Hilbert boundary value problem in the upper half of the complex plane with a countable set of coefficient discontinuities and two-side curling at infinity. We obtain a general solution in the case when the problem index has a power singularity of order $\rho$, $1/2\leq\rho1$, and study the solvability conditions.
Keywords: Riemann–Hilbert boundary value problem, curling at infinity, entire functions. 
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R. B. Salimov; P. L. Shabalin. A homogeneous Hilbert problem with discontinuous coefficients and two-side curling at infinity of order~$1/2\leq\rho<1$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2012), pp. 67-71. http://geodesic.mathdoc.fr/item/IVM_2012_11_a5/

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

[2] 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

[3] Salimov R. B., Shabalin P. L., “K resheniyu zadachi Gilberta s beskonechnym indeksom”, Matem. zametki, 73:5 (2003), 724–734 | DOI | MR | Zbl

[4] Salimov R. B., Shabalin P. L., “Metod regulyarizuyuschego mnozhitelya dlya resheniya odnorodnoi zadachi Gilberta s beskonechnym indeksom”, Izv. vuzov. Matem., 2001, no. 4, 76–79 | MR | Zbl

[5] Salimov R. B., Shabalin P. L., Kraevaya zadacha Gilberta teorii analiticheskikh funktsii i ee prilozheniya, Izd-vo Kazansk. matem. o-va, Kazan, 2005

[6] Salimov R., Shabalin P., “The Riemann–Hilbert boundary value problem with a countable set of coefficient discontinuities and two-side curling at infinity of order less than $1/2$”, Operator Theory: Advances and Applications, 221, Springer, Basel, AG, 2012, 571–585 | MR

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