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