带约束导数值域的L逼近

1972年J.A.Roulier和G.D.Taylor研究了带约束导数值域的一致逼近,在文章最后,他们提出了一个未解决的问题,就是关于带约束导数值域的L逼近问题.本文研究了这个问题,得到与[1]平行的结果.这个结果同时也推广了 R.A.Lorentz的工作. 第一节给出存在定理,第二节证明若干特征定理,第三节给出一个唯一性定理.

LAPPROXIMATION BY POLYNOMIALS WITH RESTRICTED RANGES OF THEIR DERIVATIVES

In 1972 Roulier-Taylor [1] studied the problem of uniform approximation bypolynomials with restricted ranges of their derivatives. They proposed as an openquestion the same problem of L approximation. In the present paper we investigatethis problem and obtain a set of results under the similar assumptions as in [1]. Itappears that our results are including the corresponding results of R. A. Lorentz [5]as a special case. The existence theorem of best L approximation is stated and some characterizationtheorems are proved. Furthermore, an unicity theorem is given.