自伴微分算子组离散谱的两个估计式

Two Estimating Formulas of Discrete Spectrum for Self-Adjoint Differential Operator System

考虑一类线性自伴高阶微分算子组离散谱的带权估计,利用Sturm-Liouville理论、测试函数和Rayleigh原理等方法,获得用前n个谱来估计第n+1个谱上界的一个隐式和一个显式不等式,其界与算子组的系数及权函数有关,而与所论区间的度量无关.

In this paper, weighted estimate of discrete spectrum for a class of linear self - adjoint, higher - order differential operator system is considered. Both implicit and explicit inequalities of the upper bound of the （n ＋ 1）th spectrum are estimated from the former n spectra by using Sturm - Liouville theory, matrix operation, in-tegration by parts, trial function and Rayleigh theorem etc. The bounds are related to the coefficients and weight functions of the system, but not to the measure of the interval.