Frames in generalized Fock spaces

Let A denote a real linear transformation on C n which is symmetric and positive-definite relative to the real inner product Re 〈 z , w 〉 , z , w ∈ C n . Let F A ( C n ) denote the Fock space consisting of holomorphic functions on C n which are square integrable with respect to the Gaussian measure d μ A ( z ) = det R A π n e − Re 〈 A z , z 〉 . For w ∈ C n , let e w A ( z ) = e A ( z , w ) = e − 1 2 Re 〈 A w , w 〉 K A ( z , w ) , z ∈ C n , where K A is the reproducing kernel for F A ( C n ) . The main aim of this paper is to show that there exist a , b > 0 such that the set of functions { e m a + i n b A : m , n ∈ Z n } forms a frame in F A .