Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 32-35
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A. A. Belyaev. The mean value theorem for harmonic functions in a domain of Hilbert space. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 32-35. http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a8/
@article{VMUMM_1982_5_a8,
author = {A. A. Belyaev},
title = {The mean value theorem for harmonic functions in a domain of {Hilbert} space},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {32--35},
year = {1982},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a8/}
}
TY - JOUR
AU - A. A. Belyaev
TI - The mean value theorem for harmonic functions in a domain of Hilbert space
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 1982
SP - 32
EP - 35
IS - 5
UR - http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a8/
LA - ru
ID - VMUMM_1982_5_a8
ER -
%0 Journal Article
%A A. A. Belyaev
%T The mean value theorem for harmonic functions in a domain of Hilbert space
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 1982
%P 32-35
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a8/
%G ru
%F VMUMM_1982_5_a8
We prove that the value of any harmonic function whose domain is an open set in the Hilbert space in a given point $x$ is equal to the mean value of the function with respect to a measure given on a ball with the centre $x$. From this we derive a theorem of Liouville that says that a bounded harmonic function defined in all points of a Hilbert space is constant.
