ON HADAMARD TYPE POLYNOMIAL CONVOLUTIONS WITH REGULARLY VARYING SEQUENCES

Abstract. For a sequence of polynomials Pn(x):= mn pmxm, n 1, we give a neces-sary and sufficient condition for the asymptotic equivalence P (α) n (x):= mn cmpmx m ∼ cnPn(x) (n →∞), to hold for each x A and an arbitrary regularly varying sequence {cn} of index α ∈ R