Abstract
It is found the spectrum of a singular integral operator on the compound contour with elliptic function in the kernel. Explicit solution of the corresponding singular integral equation is constructed by applying its reduction to the boundary value problem on the Riemann surface.
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References
N. I. Akhiezer, Elements of the Theory of Elliptic Functions (AMS, Providence, Rhode Island, 1990).
F. D. Gakhov, Boundary Value Problems, 3rd ed. (Nauka, Moscow, 1977) [in Russian].
T. I. Gatalskaya, “Explicit solution of Riemann boundary value problem for double periodic functions in the case of compound contour,” Math. Model. Anal. 8, 13–24 (2003).
I. Gohberg and N. Krupnik, One-Dimensional Linear Singular Integral Equations (Birkhauser, Basel, 1992), Vol. 1.
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover Books in Mathematics (Dover, New York, 1999).
V. Hutson and J. S. Pym, Applications of Functional Analysis and Operator Theory (Academic, London, 1980).
E. I. Zverovich, “Boundary value problems in the theory of analytic functions in Hölder classes on Riemann surfaces,” Russ. Math. Surv. 26, 117–192 (1971).
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Submitted by A. M. Elizarov
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Maslyukova, T.I., Rogosin, S.V. Explicit Solution to an Integral Equation with Elliptic Function in the Kernel. Lobachevskii J Math 40, 2090–2094 (2019). https://doi.org/10.1134/S1995080219120096
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DOI: https://doi.org/10.1134/S1995080219120096