In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth have been obtained in terms of approximation and interpolation errors.
We introduce the concept of asymptotic stability for a set of complex functions analytic around the origin, implicitly contained in an earlier paper of the first mentioned author (“Finite group actions and asymptotic expansion of ", Combinatorica 17 (1997), 523 – 554). As a consequence of our main result we find that the collection of entire functions with the set of all real polynomials satisfying Hayman’s condition is asymptotically stable. This answers a question raised in loc. cit.