A homogeneous Hilbert problem with a~countable set of discontinuity points of coefficients and a~logarithmic singularity of index
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 83-88.

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

We consider the Hilbert problem for the upper half-plane with a countable set of discontinuity points of coefficients of the boundary condition and with a two-side curling at infinity of a logarithmic order. We obtain formulas for the general solution to the problem.
Keywords: Riemann–Hilbert boundary value problem, curling at infinity, infinite index, entire function.
@article{IVM_2013_12_a8,
     author = {R. B. Salimov and P. L. Shabalin},
     title = {A homogeneous {Hilbert} problem with a~countable set of discontinuity points of coefficients and a~logarithmic singularity of index},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {83--88},
     publisher = {mathdoc},
     number = {12},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_12_a8/}
}
TY  - JOUR
AU  - R. B. Salimov
AU  - P. L. Shabalin
TI  - A homogeneous Hilbert problem with a~countable set of discontinuity points of coefficients and a~logarithmic singularity of index
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 83
EP  - 88
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_12_a8/
LA  - ru
ID  - IVM_2013_12_a8
ER  - 
%0 Journal Article
%A R. B. Salimov
%A P. L. Shabalin
%T A homogeneous Hilbert problem with a~countable set of discontinuity points of coefficients and a~logarithmic singularity of index
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 83-88
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_12_a8/
%G ru
%F IVM_2013_12_a8
R. B. Salimov; P. L. Shabalin. A homogeneous Hilbert problem with a~countable set of discontinuity points of coefficients and a~logarithmic singularity of index. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2013), pp. 83-88. http://geodesic.mathdoc.fr/item/IVM_2013_12_a8/

[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 | Zbl

[3] 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

[4] 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

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

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

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

[8] 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 $1/2$”, Spectral theory, mathematical system theory, evolution equations, differential and difference equations, Operator Theory: Advances and Applications, 221, Springer Basel AG, 2012, 571–585 | MR

[9] 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 | Zbl