Literature cited
P., Levi, Concrete Problems of Functional Analysis [in Russian], Nauka, Moscow (1967).
M. N. Feller, “Infinite-dimensional Laplace-Levi differential operators,” Ukr. Mat. Zh.,32, No. 1, 69–79 (1980).
R. H. Cameron and W. T. Martin, “The orthogonal development of nonlinear functional s in series of Fourier-Hermite functionals,” Ann. Math.,48, No. 2, 385–392 (1947).
N. Wiener, Nonlinear Problems in the Theory of Stochastic Processes [Russian translation], IL, Moscow (1961).
Yu. L. Daletskii and S. N. Paramonova, “Integration by parts with respect to measures in a function space. I,” Teor. Veroyatn. Mat. Stat.,17, 51–61 (1977).
G. E. Shilov and Fan Dyk Tin, Integral. Measure and Derivative on Linear Spaces [in Russian], Nauka, Moscow (1967).
D. L. Doob, Stochastic Processes [Russian translation], IL, Moscow (1956).
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag (1966).
M. N. Feller, “On infinite-dimensional elliptic operators,” Dokl. Akad. Nauk SSSR,205, No. 1, 36–39 (1972).
M. N. Feller, “On the solvability of infinite-dimensional elliptic equations with constant coefficients,” Dokl. Akad. Nauk SSSR,214, No. 1, 59–62 (1974).
M. N. Feller, “On the solvability of infinite-dimensional elliptic equations with non-constant coefficients,” Mat. Zametki,25, No. 3, 419–424 (1979).
M. N. Feller, “On the solvability of infinite-dimensional self-adjoint elliptic equations,” Dokl. Akad. Nauk SSSR,221, No. 5, 1046–1049 (1975).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 35, No. 2, pp. 200–206, March–April, 1983.
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Feller, M.N. Infinite-dimensional self-adjoint Laplace-Levi operators. Ukr Math J 35, 172–177 (1983). https://doi.org/10.1007/BF01088930
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DOI: https://doi.org/10.1007/BF01088930