Rational functions associated with the white noise space and related topics

TL;DR

This paper introduces and studies rational functions within Hida's white noise space, replacing classical bases and products with Hermite function-based bases and Wick products, inspired by hyper-holomorphic analysis.

Contribution

It extends the concept of rational functions to the white noise space setting using Hermite functions and Wick products, bridging stochastic analysis and rational function theory.

Findings

Defined rational functions in white noise space using Hermite functions.

Replaced classical Cauchy-Kovalevskaya product with Wick product.

Established foundational properties of these rational functions.

Abstract

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.