Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

[摘要] We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f,g)s = [f,g] + lambda[f',g'] where [f,g] = integral(-1)(1) f(x)g(x)(1-x(2))(alpha-1/2) dx With alpha> -1/2 and lambda>0. The asymptotics of the zeros and norms of these polynomials are also established.

[发布日期] 1997-07-08

[关键词] Sobolev orthogonal polynomials;asymptotics