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Sampling inequalities give a precise formulation of the fact that a differentiable function cannot attain large values if
its derivatives are bounded and if it is small on a sufficiently dense discrete set. Sampling inequalities can be applied
to the difference of a function and its reconstruction in order to obtain (sometimes optimal) convergence orders for very
general possibly regularized recovery processes. So far, there are only sampling inequalities for finitely smooth functions,
which lead to algebraic convergence orders. In this paper, the case of infinitely smooth functions is investigated, in order
to derive error estimates with exponential convergence orders. 相似文献