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The Riemann Problem with a Condition on the Real Axis for Generalized Analytic Functions with a Singular Curve

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Abstract

We study the inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on the real axis for one generalized Cauchy–Riemann equation with singular coefficient. For solving the problem, we deduce a structural formula for the general solution to the equation and carry out a complete study of the solvability of the Riemann boundary value problem of the theory of analytic functions with infinite index that appears because of the two points of rotation of logarithmic order. Furthermore, we deduce the formula of the general solution and study the existence and number of solutions to the boundary value problem for generalized analytic functions.

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Authors and Affiliations

  1. Kazan State University of Architecture and Engineering, Kazan, Russia

    P. L. Shabalin & R. R. Faizov

Authors
  1. P. L. Shabalin
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  2. R. R. Faizov
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Correspondence to P. L. Shabalin.

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Translated from Sibirskii Matematicheskii Zhurnal, 2023, Vol. 64, No. 2, pp. 449–462. https://doi.org/10.33048/smzh.2023.64.215

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Shabalin, P.L., Faizov, R.R. The Riemann Problem with a Condition on the Real Axis for Generalized Analytic Functions with a Singular Curve. Sib Math J 64, 431–442 (2023). https://doi.org/10.1134/S0037446623020155

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  • DOI: https://doi.org/10.1134/S0037446623020155

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