关于一类具有中间亏指数的正系数的对称微分算子

本文研究了一类具有中间亏指数的正系数的对称微分算式＝０（－１）ｋＤｋｅａｎｘＤｋ及＝０（－１）ｋａｋＤｋｅａｎｘＤｋ，证明了它们的亏指数的值域是（ｎ，ｎ＋２，…，２ｎ－１）或｛ｎ，ｎ＋ ２，…，２ｎ－２ ｝，或是一个子集合，并给出了具中间亏指数的算式的例子·这些例子表明具正系数的对称微分算式不一定都是极限点的，从而对 Ｅｖｅｒｉｔｔ Ｗ． Ｎ．［１］提出的猜测又以一种新的方式给出了否定的回答．本文还得到了一类非对称的微分算式一些相应的结果．

A Class of Positive Coefficient Ordinary Differential Operators with Middle Deficiency Indexes

In the paper, we considered a class of ordinary differential expressions as following:=0(-1)kDkeanxDk and =0(-1)kakDkenxDk, proved that their indexes are {n, n + 2,..., 2n- l} or {n, n + 2,..., 2n-2} or a subset of them, and gave some examples of positive coefficient ordinary differential operators with middle deficiency indexes. These examples show that positive coefficient ordinary differential operators needn't to be all limit-point, this is, we give a negative answer to Everitt's conjecture in another way.