Mean convergence of Lagrange interpolation

2022/06/16 by Glenier Bello, Bello, Glenier, Manuel Bello-Hernández +1 · 1 citation
Mathematics · #30A10 #41A05 (Primary) #41A10 (Secondary) #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2206.08279

openalex publication_date 2022/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove mean convergence of Lagrange interpolation at the zeros of para-orthogonal polynomials for measures in the unit circle which does not belong to Szegő's class in the unit circle. When the measure is in Szegő's class mean convergence of Lagrange interpolation is proved for functions in the disk algebra.

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• Approximation by Certain Complex Nevai Operators : Theory and Applications

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