It is well known that the image of L2(Rn) under the Hermite semigroup e- t H is a Bergman space Ht(Cn) with the reproducing kernel Lt, for t> 0. In this paper, it is shown that the discrete system { ea p + i b q , t: p, q∈ Zn} , for a, b> 0 , arising out of Lt turns out to be a frame for Ht(Cn) iff ab< πsinh 4 t. A similar type of problem is also discussed for Bessel sequences and frames in holomorphic Sobolev spaces associated with the Hermite semigroup. An attempt is also made to study a similar type of problem for the Bergman space Bt∗(C2n), which is the image of L2(Cn) under the special Hermite semigroup. © 2016, Springer International Publishing.