  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.
