N A ] 2 6 A pr 2 02 2 A SHARP UPPER BOUND FOR SAMPLING NUMBERS IN L

The general question of how well point-wise evaluations perform for approximating a function, which is often called sampling recovery or approximation using standard information, is a classical question in theoretical and applied mathematics. A historical treatment and various basics may be found in the monographs [5, 26, 27, 28, 31, 32]. It is of particular interest to compare the power of function evaluations with the power of optimal linear measurements (which could be Fourier coefficients or derivatives), since the latter are well understood in many cases and easier to handle from a theoretical point of view.