Optimal recovery of isotropic classes of twice-differentiable functions defined on d-dimensional Euclidean space

In the paper, inspired by the works of V. F. Babenko, S. V. Borodachov and D. S. Skorokhodov, we consider the problem of optimal recovery of isotropic classes of twice-differentiable multivariate functions defined on Euclidean space Rd, and get some exact results. This problem is connected with the optimal covering of Rd in discrete geometry. What Babenko et al. considered is the same kind of the optimal recovery problem of an isotropic class of twice-differentiable multivariate functions defined on a compact set of Rd and an isotropic class of twice-differentiable periodic functions.