自伴椭圆微分算子组广义谱的上界  

Upper bound of generalized spectra for self-adjoint elliptic differential operator system

作　　者：黄振明[1] HUANG Zhen-ming(Department of Mathematics and Physics, Suzhou Vocational University, Suzhou 215104, China)

机构地区：[1]苏州市职业大学数理部,江苏苏州215104

出　　处：《湖北师范大学学报（自然科学版）》2022年第2期1-7,共7页Journal of Hubei Normal University：Natural Science

摘　　要：依据Sturm-Liouville定性理论,在有界区域上对一类高阶自伴算子组的广义离散谱进行带权估计,借助特征向量空间的性质、正定矩阵的运算性质、分部积分法和测试函数法,证明了问题的离散谱与相应特征向量间存在的几个关系式,发现了特征向量满足的不等式,并估算了两个辅助积分项的上界或下界,最终获得了估计第n+1个谱上界的一个显式和一个隐式万有不等式,其结果推广了参考文献中有关低阶算子组离散谱的估计结论。Weighted estimate of generalized discrete spectra for a kind of higher-order self-adjoint operator system on bounded region is considered according to Sturm-Liouville qualitative theory.Several related expressions existing between the discrete spectra and its corresponding eigenvector are proved.The inequality satisfied by eigenvector is found.The upper or lower bounds of two auxiliary integral terms are also estimated by the help of property of eigenvector space,operational property of definite matrix,integration by parts and test function method.Finally,both explicit and implicit universal inequalities estimating the upper bound of the(n+1)th spectrum are obtained.The results are the further extension to those of lower order operator system in the bibliography.

关 键 词：自伴算子组 谱上界 Sturm-Liouville理论 特征向量空间 权函数 

分 类 号：O175.9[理学—数学]