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Characterizing orthogonality measures on the bounded interval. (English) Zbl 1160.33009

Authors’ 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 also to the Szegő class.

MSC:

33C47 Other special orthogonal polynomials and functions
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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