共查询到19条相似文献,搜索用时 86 毫秒
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本文定义了非重交换的联合半亚正常算子组,证明了谱分割定理和谱投影定理,提示了半亚正常算子组的 Taylor 联合谱与它们的记号算子组的 Taylor 联合谱之间的关系. 相似文献
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陈晓漫 《数学年刊A辑(中文版)》1989,(3)
本文讨论了亚正常算子和半亚正常算子的记号算子的摄动不变性,得到了多种形式的记号算子的摄动不变性定理。特别,若φ是可允许函数,则亚正常及半亚正常算子的记号算子关于φ摄动不变。作为应用,本文得到了一类拟亚正常算子的记号算子(它们是正常算子)的谱表示定理。 相似文献
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苏维钢 《纯粹数学与应用数学》2006,22(3):330-334,340
讨论两个拟相似半控制算子的本质谱之间的关系,应用算子谱的精密结构的分析方法,给出拟相似半控制算子的本质谱相等的若干充分条件,所得结果改进和发展了L.R.W illiam s在文[7-8]中的有关结果. 相似文献
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本文证明了每一个p-亚正常算子A,都相应存在一个亚正常算子 ,使得A与 有相同的闭值域点、相同的本质谱和谱.由此推出如果A是p-亚正常算子,B是任一有界线性算子,若存在有界线性算子X有稠值域,使得XB=AX,则σ(A)(B)此外还证明了,如果A是p-亚正常算子且 R(A)闭或KerA=KerA*, B是任一有界线性算子,A与B拟相似,则e(A)(B). 相似文献
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证明了在Hilbert空间中拟相似的闭稠定线性算子有相同的点谱、剩余谱、对于拟相似的闭形式亚正规算子还有相同的连续谱。 相似文献
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Hilbert空间加权移位及亚正规算子的可分解性 总被引:1,自引:0,他引:1
孙善利 《数学年刊A辑(中文版)》1984,(5)
本文考察了两类具体算子的谱分解,一类是Hilbert空间上加权移位算子,一类是亚正规算子,指明这两类算子可分解性的条件。 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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The purpose of this paper is to provide a detailed treatment of some subsets of Schechter's essential spectrum of closed, densely defined linear operators subjected to additive perturbations. Our results are used to describe the essential approximate point spectrum and the essential defect spectrum of singular neutron transport operators in bounded geometries. 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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该文得到了一类无穷维Hamilton算子的剩余谱和点谱存在的几个判别准则,从而给出了求其剩余谱和点谱的方法. 在此基础上构造了L^2*L^2中无穷维Hamilton算子的剩余谱非空的具体例子, 从而进一步验证了判别准则的有效性. 相似文献
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We consider upper-triangular 2-by-2 operator matrices and are interested in the set that has to be added to certain spectra of the matrix in order to get the union of the corresponding spectra of the two diagonal operators. We show that in the cases of the Browder essential approximate point spectrum, the upper semi-Fredholm spectrum, or the lower semi-Fredholm spectrum the set in question need not to be an open set but may be just a singleton. In addition, we modify and extend known results on Hilbert space operators to operators on Banach spaces. 相似文献
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H. Behncke 《Journal of Difference Equations and Applications》2013,19(5):821-829
We show that the operators whose coefficients are approximately constant in a general sense have an absolutely continuous spectrum which is equal to that of the corresponding constant coefficient operator. For such operators, the absolutely continuous spectrum can be read off from the associated characteristic polynomial. This generalizes the classical results on second-order operators and extends those of higher order differential operators to the difference setting. Our approach relies on an analysis of the associated difference equation with the help of uniform asymptotic summation techniques. 相似文献
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