Asymptotic behaviour of orthogonal polynomials relative to measures with mass points. (English) Zbl 0791.42016

Guadalupe, José J.; Pérez, Mario; Ruiz, Francisco J.; Varona, Juan L.

Mathematika 40, No. 2, 331-344 (1993).

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.

Reviewer: J.J.Guadalupe (Zaragoza)

MSC:

42C10

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

Keywords:

asymptotic estimates; orthogonal polynomials; Nevai’s class; mass point; generalized Jacobi weight

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