Approximation Theorems for Positive Linear Operators Associated with Hermite and Laguerre Polynomials

Grażyna Krech ()
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Grażyna Krech: AGH University of Science and Technology, Faculty of Applied Mathematics

A chapter in Advances in Summability and Approximation Theory, 2018, pp 141-155 from Springer

Abstract: Abstract We present some results regarding positive linear operators associated with Hermite and Laguerre expansions. We consider Poisson type integrals for orthogonal expansions and discuss their approximation properties in the $$L^p$$ space. We also investigate operators of Szász–Mirakjan type defined via Hermite polynomials. We give the rates of convergence by means of the modulus of continuity and moduli of smoothness. We present Voronovskaya type theorems for these operators and discuss boundary value problems for Poisson integrals. We also consider some combinations of the operators presented here, study their approximation errors and prove the Voronovskaya type formula.

Keywords: Poisson integrals; Linear operators; Hermite and Laguerre expansions; Approximation order; Voronovskaya type theorem; Primary 41A25; Secondary 41A36 (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-13-3077-3_8

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DOI: 10.1007/978-981-13-3077-3_8

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