Operators on the vanishing moments subspace and Stieltjes classes for M-indeterminate probability distributions

Abstract

PurposeIn this work the author gathers several methods and techniques to construct systematically Stieltjes classes for densities defined on R+.Design/methodology/approachThe author uses complex integration to obtain integrable functions with vanishing moments sequence, and then the author considers some operators defined on the vanishing moments subspace.FindingsThe author gather several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. The author constructs explicitly Stieltjes classes with center at well-known probability densities. The author gives a lot of examples, including old cases and new ones.Originality/valueThe author computes the Hilbert transform of powers of |ln⁡x| to construct Stieltjes classes by using a recent result connecting the Krein condition and the Hilbert transform.