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Статья
2021

Inhomogeneous Hilbert Boundary Value Problem with Several Points of Logarithmic Turbulence


P. L. ShabalinP. L. Shabalin, A. Kh. FatykhovA. Kh. Fatykhov
Русская математика
https://doi.org/10.3103/S1066369X21010059
Abstract / Full Text

In the unit disk, we consider the Hilbert boundary value problem. Its coefficient is assumed to be Hölder continuous everywhere on the unit circle excluding a finite set of points. At these points, the argument of the coefficient has non-removable discontinuity of logarithmic order. We obtain formulas for the general solution and fully describe the solvability of the problem in the class of functions, analytic and bounded in the unit disc. Our technique is based on the theory of entire functions of zero proximate order and the geometric theory of functions of a complex variable. We apply the obtained results to the study of the solvability of a boundary value problem for generalized analytic function.

Author information
  • Kazan State Architecture and Civil Engineering University, 1 Zelyonaya str., 420043, Kazan, RussiaP. L. Shabalin & A. Kh. Fatykhov
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