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The Riemann Problem in a Half-Plane for Generalized Analytic Functions with a Singular Line

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Abstract

In this paper we have studied an 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 coefficients. To solve this problem, we derived a structural formula for the general solution to the generalized equation and conducted a complete study of the solvability of the Riemann boundary value problem of the theory of analytic functions with an infinite index of logarithmic order. Based on the results of this study, we derived a formula for a general solution and studied the existence and the number of solutions to boundary value problems for generalized analytical functions.

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Authors and Affiliations

  1. Kazan State University of Architecture and Engineering, 420043, Kazan, Russia

    P. L. Shabalin & R. R. Faizov

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

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Shabalin, P.L., Faizov, R.R. The Riemann Problem in a Half-Plane for Generalized Analytic Functions with a Singular Line. Russ Math. 67, 66–75 (2023). https://doi.org/10.3103/S1066369X23030052

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  • DOI: https://doi.org/10.3103/S1066369X23030052

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