Characterizing orthogonality measures on the bounded interval¹

Abstract

The aim of this paper is to characterize a new class of measures on the bounded interval, which contains the semiclassical class. The characterizations are given in terms of the differential properties of the Stieltjes function and also in terms of the differential properties of the formal series of moments associated with the Chebyshev basis of first kind. We also present several interesting examples and we obtain the differential equations satisfied by the family of orthogonal polynomials when the measure belongs to the Szegö class.