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

Abstract

Purpose – In this work the author gathers several methods and techniques to construct systematically Stieltjes classes for densities defined on R+. Design/methodology/approach – The 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. Findings – The 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/value – The 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.

Keywords

• M-indeterminate density
• Stieltjes class
• Vanishing moments subspace
• Hilbert transform