We consider multivariate approximation problems in the average case setting with a zero mean Gaussian measure whose covariance kernel is a periodic Gevrey kernel. We investigate various notions of algebraic tractability and exponential tractability, and obtain necessary and sufficient conditions in terms of the parameters of the problem.

翻译：我们研究了平均情形设置下的多变量逼近问题，其中采用零均值高斯测度，其协方差核为周期Gevrey核。我们探讨了代数可解性与指数可解性的多种定义，并根据问题参数给出了必要与充分条件。