L_1尺度下周期可微函数类和卷积类的相对宽度

RELATIVE WIDTHS OF THE CLASS OF DIFFERENTIABLE FUNCTIONS AND THE PERIODIC CONVOLUTION CLASS IN L_1 METRIC

研究了由仅有实根的r次实系数代数多项式Pr(x)导出的微分算子所确定的周期可微函数类W1Pr在L1尺度下的相对宽度,得到了Kn(W1Pr,W1Pr,L1)的渐进估计.在此基础上,研究了以PF密度的周期化函数为核的周期卷积类M1(G)在L1尺度下的相对宽度,通过一个极限过程,得到了Kn(M1(G),M1(G),L1)的渐进估计.

The relative width in L1 metric of differentiable functions as defined by a real algebraic polynomial differential operator Pr（x） with real toots is studied, with asymptotic estimate of Kn （W1^Pr, W1^Pr, L1） obtained. Furthermore, the periodic convolution class M1 （G） with a kernel which is the periodization of a PF density is considered. Through a limiting process, the asymptotic estimate of Kn （M1 （G）,M1 （G）,L1 ） is obtained.