L_2(R^2;e^(-x^2-y^2))中一个特殊函数类的Kolmogorov n-宽度及最佳逼近的界的估计

Estimates of the bounds of best approximation and Kolmogorov n-width of a special class of functions in L_2(R^2;e^(-x^2-y^2))

利用一个平移算子Fh定义了高阶差分Δhk(f),进而定义广义连续模Ωk(f;δ),在空间L2(R2;e-x2-y2)中引入一个二阶微分算子D,由此来定义函数类Wφr,k(D).借鉴文献[1]中的一些结论及研究方法来研究类似文献[5-7]中所讨论的问题,最后得到了supf∈Wγφ,k(D)En(f;L2)和dn(Wωγ,k(D);L2)界的估计.

In this paper, the high-order difference Δ^kh （f） is defined by a translation operator Fh. Then the generalized modulus of continuity Ωk（f;δ） is defined. A second order differential operator D is introduced in L2（R^2;e^-x^2-y^2）,by which the function class W^r,kφ（D） is defined. The conclusions and research methods in reference[1] are used to study problems discussed in references [5] [6] [7]. At last, the bounds of supf∈Wγφ,k（D）En（f;L2） and dn（W^γ,kω（D）;L2） are estimated.