The Outer Functions In The Fock Space

This paper first discusses a kind of order in the Fock space, which means for anypolynomial p, if f(z), g(z)∈F2and pf≤pg, then f g. In particular, whenwe presents a complete characterization. As applications, we proved thatwhen|α|≥2, z+α is an outer function; however, when|α|<2, z+α is not outerfunction. our results show that the outer functions in the Fock space is not sure to becyclic vector for the Fock space, which have substantial distinction with Hardy andBergman sapces.