95-499 Kondratiev Y.G., Streit L., Westerkamp W., Yan J.

Generalized Functions in Infinite Dimensional Analysis (390K, PostScript) Nov 23, 95

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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.

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