On the tractability of linear tensor product problems in the worst case (Q731971)

The authors give a response top the following problem, namely, to derive a necessary and sufficient condition for a linear tensor product problem to be weakly tractable in the worst case. To that purpose they proved following: Theorem: Consider the linear tensor product problem~\(S\) in the worst case setting with \(\lambda_1=1\) and \(\lambda_2\in(0,1)\) with the absolute error criterion. Then~\(S\) is weakly tractable iff \(\lambda_n=o\big((\log\,n)^{-2}\big)\) as \(n\to\infty\), where \(\lambda_i\) are corresponding eigenvalues.