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 $max(s,t)\le 1$ in the worst case setting and for $s,t>0$ except $s=t=1$ in the average case setting.

本文致力于讨论在最坏情况和平均情况下使用解析Korobov核进行的多元逼近问题。我们考虑使用对任意连续线性函数进行有限多次求值的算法。我们研究指数收敛-$（s，Ť）$-易延展性（EC-$（s，Ť）$-WT）。我们通过填补EC-上剩余的空白来完全解决该问题$（s，Ť）$-WT。也就是说，我们获得了EC-的必要和充分条件$（s，Ť）$-WT为 $0<分（s，Ť）<\mathrm{1个}$ 和 $最高（s，Ť）\le \mathrm{1个}$ 在最坏的情况下 $s，Ť>0$ 除了 $s=Ť=\mathrm{1个}$ 在平均情况下。