Sunday, May 5, 2013

0712.3915 (Takahiro Hasebe et al.)

No Zero Divisor for Wick Product in $(S)^{\ast}$}    [PDF]

Takahiro Hasebe, Izumi Ojima, Hayato Saigo
In White Noise Analysis (WNA), various random quantities are analyzed as elements of $(S)^{\ast}$, the space of Hida distributions ([1]). Hida distributions are generalized functions of white noise, which is to be naturally viewed as the derivative of the Brownian motion. On $(S)^{\ast}$, the Wick product is defined in terms of the $\mathcal{S}$-transform. We have found such a remarkable property that the Wick product has no zero devisors among Hida distributions. This result is a WNA version of Titchmarsh's theorem and is expected to play fundamental roles in developing the \textquotedblleft operational calculus\textquotedblright in WNA along the line of Mikusi\'{n}ski's version for solving differential equations.
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