| 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科版,2020,33(1):70-75 |
| 调和算子多项式广义次谱的显式上界 |
| Explicit Upper Bound of Generalized Secondary Spectrum forPolynomials of Harmonic Operator |
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| DOI：10.12051/j.issn.1674-4942.2020.01.013 |
| 中文关键词: 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 |
| 英文关键词: polynomial of harmonic operator generalized secondary spectrum spectrum theory of operators principal
eigenfunction universal inequality |
| 基金项目: |
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| 摘要点击次数: 508 |
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| 中文摘要: |
| 对调和算子多项式的广义离散谱进行估计，运用偏微分方程理论和变分法技巧，发现
主特征函数与主谱、算子阶数之间的关系，证明主特征函数满足的恒等式，推得所选择的试验函数
与主谱、空间维数间的关系，最终获得用主谱来估计次谱上界的一个万有不等式，且估计系数与区
域的度量无关。 |
| 英文摘要: |
| 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 princi⁃
pal 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. |
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