共查询到15条相似文献,搜索用时 109 毫秒
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《数学的实践与认识》2013,(23)
运用算子直和分解法和二次型比较法研究了由2n阶复系数中含有指数函数和幂函数的微分算式所生成的J-自伴微分算子谱的离散性,得到了一类系数中含有指数函数和幂函数的J-自伴微分算子谱是离散的若干充分条件. 相似文献
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本文在研究一类高阶微分算子谱的离散性的基础上研究了2n阶实系数Euler微分算式生成的对称微分算子,进一步完善了自伴Euler微分算子的谱是离散的充分必要条件. 相似文献
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研究了两类对称微分算式生成的微分算子的谱的离散性.首先给出了一类三项四阶自共轭微分算子谱的离散性的充要条件.进而讨论了一类高阶自共轭微分算子的谱的离散性. 相似文献
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研究了具指数函数系数的2n阶实系数微分算式生成的对称微分算子,利用算子的直和分解法及不等式估计得到此类微分算子谱是离散的充分条件. 相似文献
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本文利用纳依玛克 ~[1]的方法研究了 2n阶非对称微分算子(J-对称微分算 子);得到一类极限点型的非对称微分算子(J-对称微分算子). 相似文献
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J—自共轭微分算子谱的定性分析 总被引:6,自引:0,他引:6
本文对J-自共轭微分算子谱理论研究情况做一些概要性的介绍,第一部分简要回顾了J-自共轭微分算子理论研究的发展过程,第二,三部分介绍了J-自共轭微分算子的本质谱和离散谱定性分析的主要方法和结论;第四部分扼要叙述J-自共轭微分算子其它方面的一些工作,以及J-自共轭微分算子谱理论研究中尚待解决的问题。 相似文献
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由线性微分算子确定的样条是连接多项式样条与希氏空间中抽象算子样条的重要环节,对微分算子样条的研究,既可从更高的观点揭示和概括多项式样条,又可启示我们去发现抽象算子样条的一些新的理论和应用. Green函数是研究微分算子样条的重要工具 [1],但在微分算子插值样条的计算及将样条用于数值分析中,再生核方法起着更重要的作用.文献[2][3]给出了与二阶线性微分算子插值样条有关的再生核解析表达式;由此得到了二阶微分算子插值样条与空间W_2~1[a,b]中最佳插值逼近算子的一致性;而且还利用再生核给出了Hi… 相似文献
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李树勇 《数学物理学报(A辑)》1996,16(4):391-403
该文研究一类微分算子的特征值问题及逆谱问题,证明了特征值与特征函数的存在性定理,建立了广义傅立叶理论,使用变换算子的工具研究了逆谱问题及其解. 相似文献
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In this paper, we consider differential operators of 2nd-order
a[u]=(-1)k(ak(x)u(k)(x))(k), x∈(0, ∞)
whose coefficients ak(x) are restricted by powers of ex, and give conditions on the coefficients sufficient to ensure that the spectrum is discrete; next we formulate necessary and sufficient conditions for the discreteness of the spectrum of differential operators whose coefficients ak(x) may increase as eαkx as x→∞. 相似文献
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H. Behncke 《Journal of Difference Equations and Applications》2013,19(5):677-695
The spectrum of higher even order difference operators with almost constant coefficients is determined. With appropriate smoothness and decay conditions on the coefficients, we show that singular continuous spectrum is absent and that the absolutely continuous spectrum agrees with that of the constant coefficient limiting operator. For such operators, the absolutely continuous spectrum is determined uniquely by the range of the characteristic polynomial. This result extends a similar result for even order differential operators. The methods of proof are closely related likewise. Finally, some results on fourth order operators with unbounded coefficients are shown. 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(5):2031-2038
This paper is concerned with the stability of essential spectra of singular Sturm‐Liouville differential operators with complex‐valued coefficients. It is proved that the essential spectrum of the corresponding minimal operator is preserved by perturbations small at infinity with respect to the unperturbed operator. Based on it, 1‐dimensional Schrödinger operators under local dilative perturbations are studied. 相似文献
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In this paper, the conditions are found on the coefficients that ensure the existence of the resolvent and the discreteness of spectrum for a class of singular differential operators. 相似文献
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