Approximation Characteristic Of Sobolev Space With Common Mixed Smoothness

In this paper, we investigate the approximation characteristic of multivariate Sobolev space W₂^A (T^d) with common mixed smoothness equipped with Guanssian measure in L_q (T^d)(1 < q<∞)(classical Sobolev space and Sobolev space with mixed deviative are its especial case). And the exact order of Kolmogorov widths and linear widths in probabilistic setting and average case setting are determined, namely...