Abstract
We consider the problem of optimal linear recovery for mixed partial differential operator A on the unit ball SBpθr(Tn) of the Nikol’skii–Besov space of periodic functions with mixed smoothness. We find error bounds sharp in order for optimal linear recovery of operator A on class SBpθr(Tn). As information IMδ(f) about the functions f from class SBpθr(Tn) we shall use Fourier coefficients with numbers from step “hyperbolic” cross. As the linear method using the information about Fourier coefficients, we shall consider action of the mixed partial differential operator A on the special “private” sum of decomposition on system (type as wavelets) trigonometric polynomials.
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