中文摘要：

在平均框架下研究相应于零均值高斯测度的一般多元逼近问题.我们考虑利用有限个连续线性泛函值所构造的逼近算法.基于协方差算子的特征值,我们得到了一般多元线性问题具有lnκ-弱易处理性的充分必要条件.

英文摘要：

This paper aims to study general multivariate approximation problems in the average case setting with respect to a zero-mean Gaussian measure, and the algorithm in the considered problems is to be constructed using the evaluations of finitely many linear functionals. The necessary and sufficient conditions are obtained for inK-weak tractability by means of the eigenvalues of the corresponding covariance operators.