On two polynomial inequalities. I
On two polynomial inequalities. I
复制标题
关于两个多项式不等式。
DOI：
10.1007/bf01895997
复制
发表时间：
1971
期刊：
影响因子：
--
通讯作者：
G. Freud
中科院分区：
文献类型：
--
作者：
G. Freud
定理1是MM DZRBASlAN [1]的一个定理的一个特例，MM DZRBASlAN [1]证明了from [n，（x）]< _e/2在每个有限区间内一致遵循zc~（x）= O（n 1/2），并对其它权函数给出了类似的结果。G. SZEG6 [8]. Dzrbasian的结果的特殊情况下，我们在脑海中可以很容易地推出Szeg 6的结果。反过来，通过变换x= t2/2，我们从定理1得到：
Theorem 1 sharpens a special case of a theorem of MM DZRBASlAN [1] who proved that from [n,(x)]< _e/2 follows zc~(x)= O (n 1/2) uniformly in every finite interval and gave analogous results for other weight-functions. The estimation of the derivative under the condition [n,(x)]<= e was treated by G. SZEG6 [8]. The special case of Dzrbasian's result which we have in mind could be easily deduced from Szeg6's result. In turn, by the transformation x= t2/2 we obtain from Theorem 1: