Geodesic
On solvability of homogeneous Riemann--Hilbert problem with discontinuities of coefficients and two-side curling at infinity of a~logarithmic order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2016), pp. 36-48.

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We consider the homogeneous Riemann–Hilbert boundary-value problem for upper half-plane in the situation where its coefficients have countable set of discontinuities of jump type and two-side curling at infinity of a logarithmic order. We obtain general solution and describe completely its solvability in a special class of functions for the case where the index of the problem has power singularity of a logarithmic order.
Keywords: Riemann–Hilbert boundary-value problem, curling at infinity, infinite index, entire functions of zero order. 
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R. B. Salimov; P. L. Shabalin. On solvability of homogeneous Riemann--Hilbert problem with discontinuities of coefficients and two-side curling at infinity of a~logarithmic order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2016), pp. 36-48. http://geodesic.mathdoc.fr/item/IVM_2016_1_a3/

[1] Alekna P. Yu., “Kraevaya zadacha Gilberta s beskonechnym indeksom logarifmicheskogo poryadka dlya poluploskosti”, Lit. matem. rink., 17:1 (1977), 5–11 | MR

[2] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1968 | MR

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

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

[5] Yurov P. G., “Odnorodnaya kraevaya zadacha Rimana s beskonechnym indeksom logarifmicheskogo tipa”, Izv. vuzov. Matem., 1966, no. 2, 158–163 | MR | Zbl

[6] Yurov P. G., “Neodnorodnaya kraevaya zadacha Rimana s beskonechnym indeksom logarifmicheskogo poryadka $\alpha\geq1$”, Materialy Vsesoyuznoi konferentsii po kraevym zadacham, Kazan, 1970, 279–284

[7] Yurov P. G., “Asimptoticheskie otsenki tselykh funktsii, zadannykh kanonicheskimi proizvedeniyami”, Matem. zametki, 10:6 (1971), 641–648 | MR | Zbl

[8] Alekna P. Yu., “Ob odnorodnoi kraevoi zadache Rimana s beskonechnym indeksom logarifmicheskogo poryadka dlya poluploskosti”, Lit. matem. rink., 13:3 (1973), 5–13 | MR | Zbl

[9] Alekna P. Yu., “Neodnorodnaya kraevaya zadacha Rimana s beskonechnym indeksom logarifmicheskogo poryadka $0\gamma1$ dlya poluploskosti”, Lit. matem. rink., 14:3 (1974), 5–18 | MR | Zbl

[10] Salimov R. B., Shabalin P. L., “Odnorodnaya zadacha Gilberta so schetnym mnozhestvom tochek razryva koeffitsientov i logarifmicheskoi osobennostyu indeksa”, Izv. vuzov. Matem., 2013, no. 12, 83–88 | MR

[11] Salimov R. B., Shabalin P. L., “Zadacha Gilberta. Sluchai beskonechnogo mnozhestva tochek razryva koeffitsientov”, Sib. matem. zhurn., 49:4 (2008), 898–915 | MR | Zbl

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

[13] Salimov R. B., Shabalin P. L., “Odnorodnaya zadacha Gilberta s razryvnymi koeffitsientami i dvustoronnim zavikhreniem na beskonechnosti poryadka $1/2\leq\rho1$”, Izv. vuzov. Matem., 2012, no. 11, 67–71 | MR | Zbl

[14] Salimov R., Shabalin P., “Solvability of the Riemann–Hilbert boundary value problem with a two-side curling at infinity point of order less than 1”, Complex Variables and Elliptic Equations, 59:12 (2014), 1739–1757 | DOI | MR | Zbl

[15] Evgrafov M. A., Asimptoticheskie otsenki i tselye funktsii, Nauka, M., 1979 | MR