Characterization of quadratic Cauchy-Stieltjes kernel families based on the orthogonality of polynomials

摘要

In this study, we state some facts regarding the sequence of polynomials associated with a Cauchy-Stieltjes kernel family and we prove that a quadratic variance function is characterized by the property of orthogonality for these polynomials. (C) 2017 Elsevier Inc. All rights reserved.