No Zero Devisor for Wick Product in (S)∗
نویسندگان
چکیده
In White Noise Analysis (WNA), various random quantities are analyzed as elements of (S)∗, 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)∗, the Wick product is defined in terms of the 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 “operational calculus” in WNA along the line of Mikusiński’s version for solving differential equations. 2000 AMS Mathematics Subject Classification: 60H40, 44A40
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تاریخ انتشار 2007