Diagonal recovery from noisy Fourier--Hermite coefficients: exact orders of the error

We consider the recovery of functions of the weighted Wiener classes $W_s^μ$ from perturbed Fourier--Hermite coefficients in the metric of $L_\infty(\mathbb R)$. For the summation methods of the class $\mathcal S^θ$ we find error estimates on $W_s^μ$. The estimates take into account the behaviour of