Asymptotics of Sobolev orthogonal polynomials for Hermite coherent pairs

[摘要] Let Q(n) be the polynomials orthogonal with respect to the Sobolev inner product (f, g)s = integral fgd mu (0) + integralf'g'd mu (1), being (mu (0), mu (1)) a coherent pair where one of the measures is the Hermite measure. The outer relative asymptotics for Q(n) with respect to Hermite polynomials are found. On the other hand, we consider the Sobolev scaled polynomials and we obtain the Plancherel-Rotach asymptotics for those as well as a consequence about their zeros. (C) 2001 Elsevier Science B.V. All rights reserved.

[发布日期] 2001-08-01

[效力级别]  Proceedings Paper

[关键词] Sobolev orthogonal polynomials;asymptotics;symmetrically coherent pairs;Hermite polynomials;Plancherel-Rotach asymptotics