Abstract
We study conditions for convergence and the rate of convergence of random functional series from the space subφ(Ω) in various norms. The results obtained are applied to the investigation of a boundary-value problem for a hyperbolic equation with random initial conditions.
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Yu. V. Kozachenko and Yu. A. Koval’chuk, “Boundary-value problems with random initial conditions and functional series from subφ(Ω). I,” Ukr. Mat. Zh., 50, No. 4, 504–515 (1998).
G. N. Polozhii, Equations of Mathematical Physics [in Russian], Vysshaya Shkola, Moscow (1964).
V. V. Buldygin and Yu. V. Kozachenko, “On the applicability of the Fourier method to the solution of problems with random boundary conditions,” in: Random Processes in Problems of Mathematical Physics [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1979), pp. 4–35.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 897–906, July, 1998.
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Kozachenko, Y.V., Koval’chuk, Y.A. Boundary-value problems with random initial conditions and functional series from subφ (Ω). II. Ukr Math J 50, 1019–1030 (1998). https://doi.org/10.1007/BF02528831
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DOI: https://doi.org/10.1007/BF02528831