Regularization of sequences in sense of E. M. Dyn'kin

Abstract

We introduce the notion of strong regularization of positive sequences. We prove an existence criterion of regular in the sense of E.M. Dyn'kin non-quasi-analiticity minorant. The criterion is given in terms on the smallest concave majorant of the logarithm of its trace function. The proof is based on the properties of the Legendre transformation.