A note about EC-[formula omitted]-weak tractability of multivariate approximation with analytic Korobov kernels

Abstract

This paper is devoted to discussing multivariate approximation problems with analytic Korobov kernels in the worst and average case settings. We consider algorithms that use finitely many evaluations of arbitrary continuous linear functionals. We investigate exponential convergence-(s,t)-weak tractability (EC-(s,t)-WT) under the absolute or normalized error criterion. We completely solve the problem by filling the remaining gaps left open on EC-(s,t)-WT. That is, we obtain necessary and sufficient conditions for EC-(s,t)-WT for 0<min(s,t)<1 and max(s,t)≤1 in the worst case setting and for s,t>0 except s=t=1 in the average case setting.