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A biorthogonal approach to the infinite dimensional fractional Poisson measure
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In this paper, we use a biorthogonal approach to the analysis of the infinite dimensional fractional Poisson measure [Formula: see text], [Formula: see text], on the dual of Schwartz test function space [Formula: see text]. The Hilbert space [Formula: see text] of complex-valued functions is described in terms of a system of generalized Appell polynomials [Formula: see text] associated to the measure [Formula: see text]. The kernels [Formula: see text], [Formula: see text], of the monomials may be expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions. Associated to the system [Formula: see text], there is a generalized dual Appell system [Formula: see text] that is biorthogonal to [Formula: see text]. The test and generalized function spaces associated to the measure [Formula: see text] are completely characterized using an integral transform as entire functions.
World Scientific Pub Co Pte Ltd
Title: A biorthogonal approach to the infinite dimensional fractional Poisson measure
Description:
In this paper, we use a biorthogonal approach to the analysis of the infinite dimensional fractional Poisson measure [Formula: see text], [Formula: see text], on the dual of Schwartz test function space [Formula: see text].
The Hilbert space [Formula: see text] of complex-valued functions is described in terms of a system of generalized Appell polynomials [Formula: see text] associated to the measure [Formula: see text].
The kernels [Formula: see text], [Formula: see text], of the monomials may be expressed in terms of the Stirling operators of the first and second kind as well as the falling factorials in infinite dimensions.
Associated to the system [Formula: see text], there is a generalized dual Appell system [Formula: see text] that is biorthogonal to [Formula: see text].
The test and generalized function spaces associated to the measure [Formula: see text] are completely characterized using an integral transform as entire functions.
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