Literature cited
L. Gross, “Potential theory on Hilbert space,” J. Functional Anal.,1, 123–181 (1967).
N. N. Frolov, “Dirichlet's problem in Hilbert space,” Sb. Teor. Veroyatn. Mat. Statistika, Kalinin State Univ., No. 3, 200–210 (1970).
N. N. Frolov, “The first boundary-value problem for an infinite-dimensional linear differential operator of arbitrary order,” Sib. Mat. Zh.,19, No. 4, 929–941 (1978).
Ya. I. Belopol'skaya and Yu. L. Daletskii, “Diffusion processes in smooth Banach manifolds,” Tr. Mosk. Mat. O-va,37, 107–131 (1978).
H.-H. Kuo, “Stochastic integrals in abstract Wiener space,” Pac. J. Math.,41, 469–483 (1972).
A. A. Lobuzov, “The first boundary-value problem for a parabolic equation in abstract Wiener space,” Mat. Zametki,30, No. 2, 211–223 (1981).
V. I. Averbukh, O. G. Smolyanov, and S. V. Fomin, “Generalized functions and differential equations in linear spaces,” Tr. Mosk. Mat. O-va,24, 132–174 (1971).
V. V. Buldygin, The Convergence of Random Elements in Topological Spaces [in Russian], Naukova Dumka, Kiev (1980).
A. D. Venttsel', A Course in the Theory of Random Processes [in Russian], Nauka, Moscow (1975).
N. N. Vakhaniya and V. I. Tarieladze, “Covariational operators of probability measures in locally convex spaces,” Teor. Veroyatn. Primen.,23, No. 1, 3–26 (1978).
N. Bourbaki, Differentiable and Analytic Manifolds [Russian translation], Mir, Moscow (1975).
A. P. Robertson and W. Robertson, Topological Vector Spaces, Cambridge Univ. Press (1973).
N. N. Frolov, “Dirichlet's problem for elliptic differential equations with infinite-dimensional operators,” Candidate's Dissertation, Voronezh (1970).
M.-A. Meier, Probability and Potentials [Russian translation], Mir, Moscow (1973).
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Translated from Matematicheskie Zametki, Vol. 34, No. 4, pp. 629–636, October, 1983.
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Khrennikov, A.Y. Dirichlet's problem in banach space. Mathematical Notes of the Academy of Sciences of the USSR 34, 804–808 (1983). https://doi.org/10.1007/BF01157401
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DOI: https://doi.org/10.1007/BF01157401