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We comment on recent results in the field of information based complexity,which state (in a number of different settings), that approximation ofinfinitely differentiable functions is intractable and suffers from the curseof dimensionality. We show that renorming the space of infinitelydifferentiable functions in a suitable way allows weakly tractable uniformapproximation by using only function values. Moreover, the approximatingalgorithm is based on a simple application of Taylor's expansion at the centerof the unit cube. We discuss also the approximation on the Euclidean ball andthe approximation in the $L_1$-norm, which is closely related to the problem ofnumerical integration.

Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions