海南师范大学学报（自然科学版）2020，Vol.33Issue(1)：70-75,6.DOI:10.12051/j.issn.1674-4942.2020.01.013
调和算子多项式广义次谱的显式上界
Explicit Upper Bound of Generalized Secondary Spectrum for Polynomials of Harmonic Operator
黄振明1
作者信息
- 1. 苏州市职业大学 数理部,江苏 苏州 215104
- 折叠
摘要
Abstract
To estimate generalized discrete spectra for polynomials of harmonic operator,the theory of partial differential equations and the calculus of variations were used.The relationship existed among the principal eigenfunction,the principal spectrum and the order of the operator was found.The inequality satisfied by the principal eigenfunction was proved.The relationship among the selected trial functions,the principal spectrum and the space dimension was inferred.At last,a universal inequality estimating the upper bound of the secondary spectrum by the principal one was obtained.Moreover,the estimated coefficients are irrelevant to the measure of the domain.关键词
调和算子多项式/广义次谱/算子谱理论/主特征函数/万有不等式Key words
polynomial of harmonic operator/generalized secondary spectrum/spectrum theory of operators/principal eigenfunction/universal inequality分类
数理科学引用本文复制引用
黄振明..调和算子多项式广义次谱的显式上界[J].海南师范大学学报（自然科学版）,2020,33(1):70-75,6.
