"Sparse trigonometric approximation of periodic Besov classes with mixed smoothness in $L_{\infty}$"Stasyuk, SerhiiOur main interest in this talk is to study sparse trigonometric approximation for periodic multivariate functions (from Besov classes and other related smoothness classes) with mixed smoothness. We use techniques connected with hyperbolic cross approximation. Motivated by recent results on the connection to nonlinear sampling recovery, we obtain order bounds for the best $m$-term approximation with respect to the multivariate trigonometric system for considered classes in $L_{\infty}$. |
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