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Lévy’s functional analysis in terms of an infinite dimensional Brownian motion III

Published online by Cambridge University Press:  22 January 2016

Yoshihei Hasegawa
Yoshihei Hasegawa*
Affiliation:
Department of Mathematics, Nagoya Institute of Technology, Gokiso, Showa-ku, Nagoya 466, Japan
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The purpose of this paper is to define minimality of surfaces in an infinite dimensional space E by probabilistic methods with the description of the relation between minimal surfaces and harmonic functions on the space E, and to analyze purely analytic properties of a certain class of quadratic forms on the space E.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 90 , June 1983 , pp. 155 - 173
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[ 1 ] Lévy, Paul, Problèmes concrets d’analyse fonctionnelle, Gauthier-Villars, Paris, 1951.Google Scholar
[ 2 ] Bombieri, E., Theory of minimal surfaces and a counter-example to the Bernstein conjecture in high dimensions, The Courant Institute, New York Univ., 1970.Google Scholar
[ 3 ] Hasegawa, Y., Levy’s functional analysis in terms of an infinite dimensional Brownian motion I, Osaka J. Math., 19 (1982), 405–428.Google Scholar
[ 4 ] Hasegawa, Y., Levy’s functional analysis in terms of an infinite dimensional Brownian motion II, Osaka J. Math., 19 (1982), 549–570.Google Scholar
[ 5 ] Port, S. C. and Stone, C. J., Brownian motion and classical potential theory, Academic Press, New York, (1978).Google Scholar