Abstract
There are exceptionally many harmonic functions of an infinite number of variables. Using for the estimate of the infinite-dimensional Laplacian introduced by P. Levy, estimates of the germ of sums of orthogonal random variables, there are obtained optimal (in a certain sense) conditions of the harmonicity of the functions in a Hilbert space. Along with harmonicity conditions obtained earlier based on estimates of the germ of sums of dependent random variables, they allow one to encompass the manifold of harmonic functions of an infinite number of variables.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 12, pp. 1687–1693, December, 1990.
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Feller, M.N. Supply of harmonic functions of an infinite number of variables. II. Ukr Math J 42, 1521–1527 (1990). https://doi.org/10.1007/BF01060824
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DOI: https://doi.org/10.1007/BF01060824