No Zero Devisor for Wick Product in $(S)^{\ast}$}

Details No Zero Devisor for Wick Product in $(S)^{\ast}$} No Zero Devisor for Wick Product in $(S)^{\ast}$}

2007-12-23

arxiv.org/abs/0712.3915v1

Physics

Mathematical Physics

5 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

No Zero Devisor for Wick Product in $(S)^{\ast}$} does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with No Zero Devisor for Wick Product in $(S)^{\ast}$}, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and No Zero Devisor for Wick Product in $(S)^{\ast}$} will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-36306