Sobolev orthogonal polynomials in the complex plane

DOI10.1016/S0377-0427(00)00498-2zbMath0973.42015MaRDI QIDQ5929299

Guillermo López Lagomasino, I. Pérez Izquierdo, Héctor Pijeira Cabrera

Publication date: 4 April 2001

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Sobolev orthogonal polynomials\(n\)th root asymptoticszero distribution

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05)

Related Items (21)

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports ⋮ Weighted Sobolev spaces: Markov-type inequalities and duality ⋮ Zero location and asymptotic behavior for extremal polynomials with non-diagonal Sobolev norms ⋮ On generating Sobolev orthogonal polynomials ⋮ Concerning asymptotic behavior for extremal polynomials associated to nondiagonal Sobolev norms ⋮ Rational approximation and Sobolev-type orthogonality ⋮ On a class of Sobolev scalar products in the polynomials. ⋮ A simple characterization of weighted Sobolev spaces with bounded multiplication operator ⋮ Weierstrass's theorem in weighted Sobolev spaces with \(k\) derivatives ⋮ Measurable diagonalization of positive definite matrices ⋮ Analytic aspects of Sobolev orthogonal polynomials revisited ⋮ The multiplication operator, zero location and asymptotic for non-diagonal Sobolev norms ⋮ Zero location for nonstandard orthogonal polynomials ⋮ Weighted Weierstrass' theorem with first derivatives ⋮ Sobolev spaces with respect to measures in curves and zeros of Sobolev orthogonal polynomials ⋮ Boundedness properties for Sobolev inner products ⋮ Weierstrass' theorem with weights ⋮ Asymptotic zero distribution for a class of extremal polynomials ⋮ Asymptotic of extremal polynomials in the complex plane ⋮ Weighted Sobolev spaces on curves ⋮ Polynomials of least deviation from zero in Sobolev \(p\)-norm

Cites Work

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• Zero location and \(n\)th root asymptotics of Sobolev orthogonal polynomials
• Zeros and critical points of Sobolev orthogonal polynomials
• Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product
• Bernstein-Szegő's theorem for Sobolev orthogonal polynomials
• Jentzsch-Szegö Type Theorems for the Zeros of Best Approximants

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