Constructing one-parameter transformations on white noise functions in terms of equicontinuous generators |
| |
Authors: | Nobuaki Obata |
| |
Institution: | (1) Graduate School of Polymathematics, Nagoya University, 464-01 Nagoya, Japan |
| |
Abstract: | Let
be a barreled locally convex space. A continuous operator on
is called anequicontinuous generator if {
n
/n!;n=0,1,2,...} is an equicontinuous family of operators. For each equicontinuous generator a one-parameter group of operators is constructed by means of power series. There is a one-to-one correspondence between the equicontinuous generators and the locally equicontinuous holomorphic one-parameter groups of operators. If two equicontinuous generators 1, 2 satisfy 1,2]=2 for some thena1+b2 is also an equicontinuous generator for anya, b. These general results are applied to a study of operators on white noise functions. In particular, a linear combination of the number operator and the Gross Laplacian, which are natural infinite dimensional analogues of a finite dimensional Laplacian, is always an equicontinuous generator. This result contributes to the Cauchy problems in white noise (Gaussian) space.Work supported by Alexander von Humboldt-Stiftung and Japan Society for Promotion of Sciences |
| |
Keywords: | 46F25 35R15 47B38 60H99 |
本文献已被 SpringerLink 等数据库收录! |
|