用指数型整函数的最佳限制逼近

Best Restriction Approximation by Entire Functions of Exponential Type

我们研究了由仅有实零点的代数多项式导出的微分算子确定的广义Sobolev类利用指数型整函数作为逼近工具的最佳限制逼近问题.利用Fourier变换和周期化等方法,得到在L_2(R)范数下的广义Sobolev光滑函数类的相对平均宽度和最佳限制逼近的精确常数,以及当0是这个代数多项式的一个至多2重的零点时,得到最佳限制逼近在L_1(R)范数和一致范数下的广义Sobolev类的精确到阶的结果.

Abstract We studied the best restriction approximation problems using entire func- tions of exponential type as the approximation tools on some generalized Sobolev classes of smooth functions defined by the differential operator induced by an algebraic poly- nomial with only real zeros. By the methods of Fourier transform and periodization,etc, we obtained the exact constants of the average relative widths and the best restric- tion approximation on the generalized Sobolev classes in the L2（R） norm, and obtained the asymptotic results of the best restriction approximation on the generalized Sobolev classes in the L1 （R） norm and the uniform norm for the case that the polynomial has a zero of multiplicity at most 2 at the point 0.