On the approximation in the mean with the Chebyshev-Hermite weight by algebraic polynomials on the real axis

Abstract

Exact inequalities of Jackson type for the best polynomial approximation of functions in the space $L_{2,\rho}(\mathbb{R})$ with the Chebyshev -Hermite weight function have been obtained for the $m^{th}$ order generalized moduluses of continuity $\widetilde{\omega}_m, m \in \mathbb{N}$, at the classes $L^r_{2,\rho}(\mathbb{R}), r \in \mathbb{N}$