双调和算子组高阶谱的估计式  

Estimating formulas of higher order spectrum for biharmonic 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：《陕西理工大学学报（自然科学版）》2020年第6期69-74,共6页Journal of Shaanxi University of Technology:Natural Science Edition

摘　　要：考虑齐次边界条件下双调和算子组离散谱的带权估计,利用特征向量的标准正交化条件、正定矩阵的性质和运算、分部积分法和不等式估计等技巧,首先将问题化为矩阵形式,建立关于谱的一个基本不等式;其次证明离散谱与特征向量间关系的几个引理;然后得到了用前n个谱来估计第n+1个谱上界的解析不等式,该式的估计系数与区域的大小及形状无关;最后将结论推广至任意阶调和算子组。Weighted estimate of discrete spectrum for biharmonic operator system under homogeneous boundary conditions is considered.The techniques used are orthonormalization condition of eigenvector,property and operation of definite matrix,integration by parts and inequality estimate etc.First of all,we change the system into matrix form,and establish a basic spectrum inequality.Secondly,for clearness,we prove several lemmas regarding the relationship between discrete spectra and their eigenvectors.At last,the main results turn out immediately.These estimates are that the analytic inequality of the upper bound of the(n+1)th spectrum is estimated by the former n spectra.The estimate coefficients do not depend on the size or shape of the region in which the problem is concerned.The conclusions are generalized into arbitrary order harmonic operator system.

关 键 词：双调和算子组 离散谱 变分原理 标准正交化 加权空间 

分 类 号：O175.9[理学—数学]