arXiv subjects
Publications and source records attributed to Ali Reza Khatoon Abadi.
This paper presents some mathematical aspects of Classical Liouville theorem and we have noted some mathematical theorems about its initial value problem. Furthermore, we have implied on the formal frame work of Stochastic Liouville equation (SLE).
In this letter we proved this theorem: \emph{if $F$ be a holomorphic mapping of $T_Ω$ to a mapping manifold $X$ such that for every compact subset $K\subset Ω$ the mapping $F$ is uniformly continues on $T_{K}$ and $F(T_{K})$ is a relatively compact subset of $X$. If the restriction of $F(z)$ to some hyperplane $\mathbb{R}^{m}+iy'$ is semi periodic, then $F(z)$ is an semi mapping of $T_Ω$ to $X$.}
In this short paper we review and extract some features of the Fredholm Alternative problem .