Probabilistic and Average Gel’fand Widths of Sobolev Space Equipped with Gaussian Measure in the Sq-Norm

In this article, we mainly studied the Gel’fand widths of Sobolev space in the probabilistic and average settings. And, we estimated the sharp bounds of the probabilistic Gel’fand (N,δ)-widths of multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm by discretization methods. Later, we estimated the sharp bounds of the p-average Gel’fand N-widths of univariate Sobolev space W2r(T) and multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm.