K-moment problem for recursive sequences of order∞: Application to the zeros of analytic functions

In this paper we solve the K-moment problem for a family of sequences defined by linear recursive relations of order∞indexed by Z. Extension of some known properties are studied and others results are established. Moreover, we paraphrase a fundamental application on the existence of zeros of an analytic function, in terms of the support of the representing measure of the former sequences. © 2007 Elsevier Inc. All rights reserved