Approximation of generalized Poisson integrals by interpolation trigonometric polynomials

2023/03/09 by Serdyuk, Anatoly, Тетяна Степанюк, Stepaniuk, Tetiana
Mathematics · #Approximation Theory and Sequence Spaces #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2303.05568

openalex publication_date 2023/03/09 · openalex created_date 2023/03/14 · openalex updated_date 2026/07/28

Abstract

In this paper we establish asymptotically best possible interpolation Lebesgue-type inequalities for 2π-periodic functions f, which are representable as generalized Poisson integrals of the functions φ from the space L_p, 1≤ p≤ ∞. In these inequalities the deviation of the interpolation Lagrange polynomials |f(x)- S_n-1(f;x)| for every x∈ℝ is expressed via the best approximations E_n(φ)_L_p of the functions φ be trigonometric polynomials in L_p-metrics. We also find asymptotic equalities for the exact upper bounds of points approximations by interpolation trigonometric polynomials on the classes C^α,r_β,p of generalized Poisson integrals of the functions, which belong to the unit balls of the spaces L_p, 1≤ p≤∞.

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