关于上密度无限制的缺项多项式加权逼近

令Ca为由在实轴R上连续且满足f(t)exp(-a(t))→0的函数f组成的Banach空间,其中a(t)为非负连续函数.在本文中,我们得到缺项的多项式在Ca中不完备的充分条件.本文的要点在于我们不要求上密度是有限的.

On Weighted Polynomial Approximation with Unrestricted Upper Density Gaps

Let Ca be the weighted Banach space of complex continuous functions f defined on the real axis R with f(t)exp(-a(t))vanishing at infinity in the uniform norm, where a(t)is a nonnegative continuous function. In this paper, we obtain sufficient condition for polynomial with gaps not to be dense in Ca. The point here in our paper is that the gaps are not required to have a finite upper density.