Abstract
We study a periodic Riemann problem of finding a pair of analytic functions in the upper and lower half-strips and describe its solvability conditions depending on the index of the problem. We show that this problem can be used to study the solvability of discrete convolution equations.
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References
Gakhov, F.D., Kraevye zadachi (Boundary Value Problems), Moscow: Nauka, 1977.
Muskhelishvili, N.I., Singulyarnye integral’nye uravneniya (Singular Integral Equations), Moscow: Nauka, 1968.
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Original Russian Text © A.V. Vasil’ev, V.B. Vasil’ev, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 5, pp. 642–649.
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Vasil’ev, A.V., Vasil’ev, V.B. Periodic Riemann problem and discrete convolution equations. Diff Equat 51, 652–660 (2015). https://doi.org/10.1134/S0012266115050080
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DOI: https://doi.org/10.1134/S0012266115050080