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Asymptotic behaviour of orthogonal polynomials relative to measures with mass points
Author(s) -
Guadalupe José J.,
Pérez M.,
Ruiz Francisco J.,
Varona Juan L.
Publication year - 1993
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007099
Subject(s) - mathematics , orthogonal polynomials , real line , class (philosophy) , jacobi polynomials , orthonormal basis , combinatorics , pure mathematics , point (geometry) , geometry , physics , quantum mechanics , artificial intelligence , computer science
General expressions are found for the orthonormal polynomials and the kernels relative to measures on the real line of the form μ + M δ c , in terms of those of the measures d μ and ( x − c ) 2 d μ. 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 obtain several bounds for the polynomials and kernels relative to a generalized Jacobi weight with a finite number of mass points.