调和算子二次多项式广义第二谱的上界（英文）

Upper Bound of Generalized Second Spectrum for Quadratic Polynomial of Harmonic Operator

对调和算子二次多项式的低阶谱进行研究,首先,选择一组合适的试验函数,根据Rayleigh原理建立一基本不等式,其次,利用分部积分和Schwarz不等式等方法,估算若干积分项的上界或下界,最后,获得了用第一谱的线性函数来估计第二谱上界的一个万有不等式,结果显示其估计系数与区域的大小及形状无关,所得结论拓宽了参考文献中的定理,在微分算子谱估计理论中有一定的潜在应用价值.

The low order spectra for quadratic polynomial of harmonic operator is studied.Firstly,a set of suitable experimental functions is selected to establish a basic inequality according to Rayleigh principle.Secondly,the upper or lower bounds of several integral terms are estimated by means of partial integration and Schwarz inequality.Finally,a universal inequality of the upper bound of the second spectrum is estimated by using the linear function of the first spectrum.The results show that the estimation coefficients are independent of the size and shape of the region.The conclusions broaden the theorems in the references and have potential application value in the theory of spectral estimation of differential operators.