Estimates for Jacobi-Sobolev type orthogonal polynomials

1996/01/26 by Manual Alfaro, Alfaro, Manual, Francisco Marcellán +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.math/9601216

arxiv created 1996/01/26 · arxiv updated 2016/09/06

Abstract

Let the Sobolev-type inner product <f,g> = ∫ fg d mu₀+ int f' g' d mu₁ with mu₀ = w + M delta_c, mu₁= N delta_c where w is the Jacobi weight, c is either 1 or -1 and M, N >= 0. We obtain estimates and asymptotic properties on [-1,1] for the polynomials orthonormal with respect to <.,.> and their kernels. We also compare these polynomials with Jacobi orthonormal polynomials.

Related

• Asymptotic behavior of varying discrete Jacobi--Sobolev orthogonal polynomials
• Fourier series of Jacobi-Sobolev polynomial
• A new approach to the asymptotics for Sobolev orthogonal polynomials
• Sobolev orthogonal polynomials on a simplex
• Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product