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

In: Advances in Summability and Approximation Theory

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  • Grażyna Krech

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

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.

Suggested Citation

  • Grażyna Krech, 2018. "Approximation Theorems for Positive Linear Operators Associated with Hermite and Laguerre Polynomials," Springer Books, in: S. A. Mohiuddine & Tuncer Acar (ed.), Advances in Summability and Approximation Theory, pages 141-155, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-3077-3_8
    DOI: 10.1007/978-981-13-3077-3_8
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