摘要
微分算子理论是解决关于当代量子力学和数学物理方程中一些问题的重要数学工具 ,因此受到数学物理工作者的广泛关注 .在本文中主要应用分析的方法研究了在复的 Hilbert空间 L2 [0 ,1 ]上由一般情形的四阶微分算式 l( y) =y( 4) + p1y( 2 ) + p2 y( 1) + p3 y和边条件所生成的微分算子 L的特征行列式 ,及当 |λ|值充分大时特征函数的展开式 ,并对算子的 Green函数给出了一个重要的估计 .
The theory of differential operators is a forceful mathematical tool in modern quantum mechanic and mathematics physics equation.So it has been paid more attention to by mathematics and physics researchers.In this paper,We investigate by the method of analysis a class of the four order differential operators on bounded interval,which are generated by differential expression l(y)=y (4) +p 1y (2) +p 2y (1) +p 3y in complex Hilbert space L 2 with bounded conditions.We obtain some results about the characteristic determinant,eigenvector expansion for |λ| sufficiently large.And we get an important estimation for Green function of operators.
出处
《内蒙古大学学报（自然科学版）》
CAS
CSCD
北大核心
2002年第3期241-246,共6页
Journal of Inner Mongolia University：Natural Science Edition
基金
国家自然科学基金资助项目 ( 1 9871 0 37)
