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Статья
2014

The Riemann problem for functions with polar lines of higher orders


A. I. AfoninaA. I. Afonina, I. G. SalekhovaI. G. Salekhova
Русская математика
https://doi.org/10.3103/S1066369X14110012
Abstract / Full Text

We consider solutions of the jump problem, homogeneous and inhomogeneous Riemann problems for functions with polar lines of orders p k +1 (k = 1, 2, … ), p k ⩾ 0. We study the cases of continuous and discontinuous coefficients. In the special case p k = 0 the obtained results turn into the earlier known ones.

Author information
  • Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, RussiaA. I. Afonina & I. G. Salekhova
References
  1. Chibrikova, L. I., Salekhova, I. G. “The Riemann Problem in the case of countable set of contours,” in Transactions of Seminar on Boundary-Value Problems (Kazan, Kazan Univ. Press, 1972), Issue 9, pp. 216–233 [in Russian].
  2. Chibrikova, L. I. Main Boundary-Value Problems for Analytical Functions (Kazan, Kazan Univ. Press, 1977).
  3. Golubev, V. V. Single-valued Analytical Functions. Automorphic Functions (Fizmatgiz, Moscow, 1961) [in Russian].
  4. Muskhelishvili, N. I. Singular Integral Equations. Boundary-Value Problems of Theory of Functions with Certain Applications in Mathematical Physics (Fizmatgiz, Moscow, 1962) [in Russian].