Geodesic
Inhomogeneous Hilbert Boundary-Value Problem with a Finite Number of Second-Type Singularity Points
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 143-150

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In this paper, we describe the inhomogeneous Hilbert boundary-value problem of the theory of analytic functions with an infinite index and a boundary condition for a half-plane. The coefficients of the boundary condition are Hölder-continuous everywhere except for a finite number of singular points at which the argument of the coefficient function has second-type discontinuities (of a power order with exponent $1$). We obtain formulas for the general solution of the inhomogeneous problem and discuss the existence and uniqueness of the solution. The study is based on the theory of entire functions and the geometric theory of functions of a complex variable.
Keywords: Hilbert problem, Phragmén–Lindelöf principle, infinite index, entire functions. 
@article{INTO_2018_153_a10,
     author = {A. Kh. Fatykhov and P. L. Shabalin},
     title = {Inhomogeneous {Hilbert} {Boundary-Value} {Problem} with a {Finite} {Number} of {Second-Type} {Singularity} {Points}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {143--150},
     publisher = {mathdoc},
     volume = {153},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_153_a10/}
}
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A. Kh. Fatykhov; P. L. Shabalin. Inhomogeneous Hilbert Boundary-Value Problem with a Finite Number of Second-Type Singularity Points. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 143-150. http://geodesic.mathdoc.fr/item/INTO_2018_153_a10/