# No Zero Divisor for Wick Product in $S^{ast}$} - Mathematical Physics

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Abstract: In White Noise Analysis WNA, various random quantities are analyzed aselements of $S^{\ast}$, the space of Hida distributions 1. Hidadistributions are generalized functions of white noise, which is to benaturally viewed as the derivative of the Brownian motion. On $S^{\ast}$, theWick product is defined in terms of the $\mathcal{S}$-transform. We have foundsuch a remarkable property that the Wick product has no zero devisors amongHida distributions. This result is a WNA version of Titchmarsh-s theorem and isexpected to play fundamental roles in developing the \textquotedblleftoperational calculus\textquotedblright in WNA along the line ofMikusi\-{n}ski-s version for solving differential equations.

Author: Takahiro Hasebe, Izumi Ojima, Hayato Saigo

Source: https://arxiv.org/