Probabilistic and average widths of multivariate Sobolev spaces with mixed derivative equipped with the Gaussian measure

We present sharp bounds on the Kolmogorov probabilistic (N, δ)-width and p average N- width of multivariate Sobolev space with mixed derivative MW2r(Td), r = (r1 ..., rd), 1/2 1 is depending only on the eigenvalues of the correlation operator of the measure µ (see (4)).

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