Tractability of Multivariate Approximation Defined over Hilbert Spaces with Exponential Weights

Abstract

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 $\mathbf{a}=\{a_j{\}}_{j\in \mathbb{N}}$ and $\mathbf{b}=\{b_j{\}}_{j\in \mathbb{N}}$ of positive numbers, and on a bounded sequence of positive integers $\mathbf{m}=\{m_j{\}}_{j\in \mathbb{N}}$. The sequence $\mathbf{a}$ is non-decreasing and the sequence $\mathbf{b}$ is bounded from below by a positive number. We find necessary and sufficient conditions on $\mathbf{a},\mathbf{b}$ and $\mathbf{m}$ to achieve the standard and new notions of tractability in the worst case setting.

References in corpus (1)

• Notes on $(s,t)$-weak tractability: A refined classification of problems with (sub)exponential information complexity

Cited by in corpus (1)

• ${\mathbf{L}}_{\infty }$-approximation in Korobov spaces with Exponential Weights