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

  • Grażyna KrechEmail author


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.


Poisson integrals Linear operators Hermite and Laguerre expansions Approximation order Voronovskaya type theorem 

AMS 2010

Primary 41A25 Secondary 41A36 


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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Applied MathematicsAGH University of Science and TechnologyKrakówPoland

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