compact perturbations of orthogonal polynomials - Project Euclid
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compact perturbations of orthogonal polynomials - Project Euclid
polynomials of the second kind and there are explicit formulas in [9]. ..... If one uses this Wronskian formula in the previous equation, then. (3.3) a°n+ι
PACIFIC JOURNAL OF MATHEMATICS Vol. 153, No. 1, 1992
COMPACT PERTURBATIONS OF ORTHOGONAL POLYNOMIALS PAUL NEVAI AND WALTER VAN ASSCHE We investigate orthogonal polynomials on the real line defined by a recurrence relation for which the recurrence coefficients behave asymptotically like a given system of recurrence coefficients. We give the asymptotic behavior of the orthogonal polynomials (relative to the given comparison system of orthogonal polynomials) and from this we deduce properties of the orthogonality measure.
1. Introduction. Let μo be a positive unit measure on the real line such that its support contains infinitely many points and all the moments are finite. Assume moreover that the Hamburger moment problem is determined. Denote by pn(x μo) (n = 0, 1, 2, ...) the normalized orthogonal polynomials for the measure μo, i.e. Pn(x
