Tractability of multivariate approximation defined over Hilbert spaces with exponential weights

@article{Irrgeher2016TractabilityOM,
title={Tractability of multivariate approximation defined over Hilbert spaces with exponential weights},
author={Christian Irrgeher and Peter Kritzer and Friedrich Pillichshammer and Henryk Wozniakowski},
journal={Journal of Approximation Theory},
year={2016},
volume={207},
pages={301-338}
}

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… CONTINUE READING