 95499 Kondratiev Y.G., Streit L., Westerkamp W., Yan J.
 Generalized Functions in Infinite Dimensional Analysis
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Nov 23, 95

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Abstract. We give a general approach to infinite dimensional
nonGaussian 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 nondegenerate measures on
conuclear spaces with analytic characteristic
functionals. It is worth emphasizing that no further
condition such as quasiinvariance 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.
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