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 |
Keywords:
Rational functions; Hida’s white noise space; Gleason’s problem; Wick product; Hyperholomorphic functionsReferences:
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