Abstract
then it is a renewal sequence if and only if it is bounded. Since a Stieltjes moment sequence satisfies condition (1) and since it is a bounded sequence if and only if it is a HausdorR moment sequence, one is naturally led to consider the relationship between moment sequences and renewal sequences. In this note we use Loewner’s theory of monotone matrix functions to investigate the solutions of the renewal equations associated with the three classical moment problems and we obtain results which include those of T. Kaluza.
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