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 Szasz–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.
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