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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:
AMS Subject Classification (2000)::
Acknowledgements
The author is grateful to Prof. H. Ouerdiane who has given him an opportunity to discuss a new direction discussed in this report.