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Asymptotic behaviour of orthogonal polynomials relative to measures with mass points. (English) Zbl 0791.42016
General expressions are found for the orthogonal polynomials and the kernels relative to measures on the real line of the form \(\mu+ M\delta_ c\), in terms of those of the measures \(d\mu\) and \((x- c)^ 2 d\mu\). In particular, these relations allow us to show that Nevai’s class \(M(0,1)\) is closed under adding a mass point, as well as to obtain several bounds for the polynomials and kernels relative to a generalized Jacobi weight with a finite number of mass points.

MSC:
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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