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Rational functions associated with the white noise space and related topics. (English) Zbl 1203.30051
Summary: Motivated by the hyper-holomorphic case we introduce and study rational functions in the setting of Hida’s white noise space. The Fueter polynomials are replaced by a basis computed in terms of the Hermite functions, and the Cauchy-Kovalevskaya product is replaced by the Wick product.

MSC:
30G35 Functions of hypercomplex variables and generalized variables
26C15 Real rational functions
60H40 White noise theory
47A99 General theory of linear operators
32A05 Power series, series of functions of several complex variables
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