Tractability of Approximation of Functions Defined over Weighted Hilbert Spaces

We investigate L₂-approximation problems in the worst case setting in the weighted Hilbert spaces H (Kₑ_₃, , ) with weights R₃, , under parameters 1 ₁ ₂ 0 and 1₁ ₂. Several interesting weighted Hilbert spaces H (Kₑ_₃, , ) appear in this paper. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; weighted Hilbert spacesWe discuss tractability of L₂-approximation problems for the involved Hilbert spaces, which describes how the information complexity depends on d and ^-1. As a consequence we study the strongly polynomial tractability (SPT), polynomial tractability (PT), weak tractability (WT), and (t₁, t₂) -weak tractability ( (t₁, t₂) -WT) for all t₁1 and t₂0 in terms of the introduced weights under the absolute error criterion or the normalized error criterion.