Kondratiev Y.G., Streit L., Westerkamp W., Yan J.
Generalized Functions in Infinite Dimensional Analysis
(390K, PostScript)
ABSTRACT. We give a general approach to infinite dimensional
non-Gaussian Analysis. For smooth probability measures on
infinite dimensional linear spaces a biorthogonal
decomposition is a natural extension of the
orthogonal one that is well known in Gaussian analysis.
This biorthogonal ``Appell'' system has been
constructed for smooth measures by Yu.L.~Daletskii.
We consider the case of non--degenerate measures on
co-nuclear spaces with analytic characteristic
functionals. It is worth emphasizing that no further
condition such as quasi--invariance of the measure or
smoothness of logarithmic derivatives are required.
The point here is that the important example of Poisson noise
is now accessible. Within the above framework
-- we obtain an explicit description of the test function space
-- in particular this space is in fact identical for all the
measures that we consider
-- characterization theorems for generalized as well as
test functions are obtained analogously as in Gaussian analysis
-- the well known Wick product and the corresponding Wick calculus
extends rather directly
-- a full description of positive distributions (as measures)
will be given.