On Some Properties of Generalized Fock Space $F^2(dv_\alpha)$ by Frame Theory on the $C^n$

Abstract

We obtain a short and new sharp proof for atomic decomposition for Fock space on the $C^n$ by using the frame theory. In fact we show that the generalized Fock space $F^2(dv_\alpha)$ on the $C^n$ admit an atomic decomposition i.e every analytic function in this space can be presented as a linear combination of "atoms" defined using the normalized reproducing kernel of this space.