Tractability of multivariate approximation defined over Hilbert spaces with exponential weights

摘要

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 epsilon N) and b = {b(j)}(j epsilon N) of positive numbers, and on a bounded sequence of positive integers m = {m(j)}(j epsilon 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. (C) 2016 Elsevier Inc. All rights reserved.