White noise analysis and class II subgroups of the infinite dimensional rotation group

Abstract

White noise analysis uses expressions of functionals and operators in two ways, one is the so-called digital. Taking the system of basic random variables to be , functionals and operators are defined depending on those variables . The other is analogue. The system of variables is that of idealized elemental random variables , namely white noise. The first aim of this note is to see a clear passage from digital to analogue. The second aim is to find subgroups, actually sub-semigroups, of the infinite dimensional rotation group which play dominant roles in white noise analysis. Related to the analogue calculus, we shall find sub-semigroups of . They are interested in white noise analysis and in group theory too.

Keywords:

• white noise
• half whisker
• rotation group

AMS Subject Classification (2000)::

• 60H40

Acknowledgements

The author is grateful to Prof. H. Ouerdiane who has given him an opportunity to discuss a new direction discussed in this report.