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Solutions of Boundary-Value Problems for the Helmholtz Equation in Simply Connected Domains of the Complex Plane

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The bases in the spaces of functions analytic in simply connected domains are constructed with the help of conformal mappings of these domains onto a circle. The obtained basis functions are biorthogonal to the Faber polynomials. By using the expansions of analytic functions in series in systems of basis functions, we determine the solutions of boundary-value problems for the Helmholtz equation whose boundary values coincide with the boundary values of these functions.

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  1. “L’vivs’ka Politekhnika” National University, Lviv, Ukraine

    M. A. Sukhorolsky

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  1. M. A. Sukhorolsky
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 4, pp. 34–46, October–December, 2015.

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Sukhorolsky, M.A. Solutions of Boundary-Value Problems for the Helmholtz Equation in Simply Connected Domains of the Complex Plane. J Math Sci 228, 35–52 (2018). https://doi.org/10.1007/s10958-017-3604-0

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  • DOI: https://doi.org/10.1007/s10958-017-3604-0

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