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- W2776094324 abstract "We obtain a sufficient condition for subharmonicity of functions of two variables that uses Laplace difference operator of Schwartz type. M.A. Kreines proved that an upper semi-continuous function is subharmonic, if for some n ≥ 3 for every point ζ of its domain one can construct of a sufficiently small radius with the center at ζ such that the right n-gon can be inscribed in the circle, while the function value at the point ζ does not exceed the arithmetic mean of its values at the vertices of this n-gon. In this note the semi-continuity condition for the function is replaced by some conditions of function directional continuity an summability (with respect to the planar Lebesgue measure.) We also provide the position of nodes for the Laplace difference operator such that the proposition similar to the Kreines's Theorem on a sufficient condition for the subharmonicity is valid for the functions of three variables." @default.
- W2776094324 created "2018-01-05" @default.
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- W2776094324 date "2017-12-01" @default.
- W2776094324 modified "2023-09-24" @default.
- W2776094324 title "On a sufficient condition for the subharmonicity of functions, satisfying the discrete mean value inequality" @default.
- W2776094324 doi "https://doi.org/10.1088/1742-6596/937/1/012053" @default.
- W2776094324 hasPublicationYear "2017" @default.
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