Tractability of multivariate approximation defined over Hilbert spaces with exponential weights

We study multivariate approximation defined over tensor product Hilbert spaces. The space is a weighted tensor product Hilbert space with exponential weights which depend on two sequences a = { a j } j ? N and b = { b j } j ? N of positive numbers, and on a bounded sequence of positive integers m = { m j } j ? N . The sequence a is non-decreasing and the sequence b is bounded from below by a positive number. We find necessary and sufficient conditions on a , b and m to achieve the standard and new notions of tractability in the worst case setting.

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