Abstract:
We evaluate the suprema of approximation
of bivariate functions by triangular partial sums of the double
Fourier–Hermite series on the class of functions $L_{2}^{r}(D)$ in
the space $L_{2,\rho}(\mathbb{R}^2)$, where $D$ is the second-order Hermite
operator. Sharp Jackson–Stechkin type inequalities on the sets
$L_{2,\rho}(\mathbb{R}^2)$ are obtained, in which the best approximation is
estimated from above both in terms of moduli of continuity of
order $m$. $N$-widths of some classes of functions in $L_{2,\rho}(\mathbb{R}^2)$ are evaluated.
References