This is the proceedings of the 2nd Japanese-German Symposium on Infinite Dimensional Harmonic Analysis held from September 20th to September 24th 1999 at the Department of Mathematics of Kyoto University.この論文集は, 1999年9月20日から9月24日の日程で京都大学理学研究科数学教室において開催された第2回日独セミナー「無限次元調和解祈」の成果をもとに編集されたものである.編集 : ハーバート・ハイヤー, 平井 武, 尾畑 信明Editors: Herbert Heyer, Takeshi Hirai, Nobuaki Obata #enIn this paper, we give infinite dimensional stochastic processes generated by functions of the Lévy Laplacian. Moreover we introduce an operator to connect the Lévy Laplacian with the Number operator and also give a relationship between a (Co)-semigroup generated by the Lévy Laplacian and an infinite dimensional Ornstein-Uhlenbeck process
