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A characterization of the Lévy Laplacian in terms of infinite dimensional rotation groups

Published online by Cambridge University Press:  22 January 2016

Nobuaki Obata
Nobuaki Obata*
Affiliation:
Department of Mathematics, School of Science Nagoya University, Nagoya, 464-01, Japan
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P. Lévy introduced, in his celebrated books [21] and [22], an infinite dimensional Laplacian called the Lévy Laplacian in connection with a number of interesting topics in variational calculus. One of the most significant features of the Lévy Laplacian is observed when it acts on the singular part of the second functional derivatives. For this reason the Lévy Laplacian has become important also in white noise analysis initiated by T. Hida [12]. On the other hand, as was pointed out by H. Yoshizawa [29], infinite dimensional rotation groups are profoundly concerned with the structure of white noise, and therefore, play essential roles in certain problems of stochastic calculus. Motivated by these works, we aim at developing harmonic analysis on infinite dimensional spaces by means of the Lévy Laplacian and infinite dimensional rotation groups.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 118 , June 1990 , pp. 111 - 132
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

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