Geodesic
Inhomogeneous Hilbert boundary value problem with several points of logarithmic turbulence
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2021), pp. 64-80

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We consider the so called Hilbert boundary value problem with boundary condition in the unit disk. Its coficient is assumed to be Hölder-continuous everywhere on the unit circle excluding a finite set of points. At these points its argument has nonremovable discontinuity of logarithmic order. We obtain formulas for the general solution and describe completely the solvability picture in a class of analytic and bounded functions in unit disc. Our technique is based on the theory of entire functions of zero-order approximation and the geometric theory of functions. The results obtained are applied to the study of the solvability of a single boundary value problem for a certain class generalized analytic function.
Keywords: Riemann–Hilbert problem, maximum principle, infinite index, entire functions of zero-order approximation, generalized analytic function. 
@article{IVM_2021_1_a4,
     author = {P. L. Shabalin and A. Kh. Fatykhov},
     title = {Inhomogeneous {Hilbert} boundary value problem with several points of logarithmic turbulence},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {64--80},
     publisher = {mathdoc},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_1_a4/}
}
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P. L. Shabalin; A. Kh. Fatykhov. Inhomogeneous Hilbert boundary value problem with several points of logarithmic turbulence. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2021), pp. 64-80. http://geodesic.mathdoc.fr/item/IVM_2021_1_a4/