Functions satsifying the mean value property
نویسندگان
چکیده
منابع مشابه
Invariant Mean Value Property and Harmonic Functions
We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.
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where „((?)= const depending on n. In this paper we consider the converse problem, namely: Suppose (0.1) holds for all harmonic functions, is S necessarily a sphere with center P (and consequently „^const)? The answer is in general negative, unless some assumptions are made on „. Thus, (0.1) is always satisfied with „(Q) = —dG(P, Q)/dv, G being Green's function of the Laplace equation in D and ...
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We establish a mean value property for harmonic functions on the interior of a hyperbola. This property connects their boundary values with the interior ones on the axis of the hyperbola from the focus to infinity.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1962
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1962-0151628-9