共查询到18条相似文献,搜索用时 93 毫秒
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一类线性非自伴算子的谱 总被引:8,自引:1,他引:7
近年来国际上出现了一类以迁移理论为背景的所谓"u-标算子(u-scalaroperator)".本文研究u-标算子与经典的标型谱算子(spectraloperatorofscalartype)的内在联系,给出了此类算子的谱与其无界投影族之间的关系,证明了该类算子的剩余谱是空集. 相似文献
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类似与标型谱算子,U-标算子是否拟仿射相似于自伴算子是一“公开问题”.尽管对具纯离散谱的U-标算子答案是肯定的,但一般情况下并不成立.本文继续探讨这一问题,证明了U-标算子在一强范数拓扑意义下是Hermite算子,或者说U-标算子拟仿射相似于Hermite算子,并给出U-标算子是标型谱算子的充要条件. 相似文献
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本文给出了U-标算子经连续算子演算后有界的充分条件。另外,对一给定的U-标算子T,证明了当函数μ(t)连续可导时算子μ(T)有界,但存在连续函数使得μ(T)无界。 相似文献
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本文研究了具有有限升标(降标)的半Fredholm算子,证明了具有有限 升标(降标)的上半Fredholm算子在其摄动类中交换元的摄动下仍具有同样性质,对于下半Fredholm算子有同样结论。从而改进了[1,2]中的主要结果。同时,我们证明了被摄动算子集合扩大(相对于[1]而言)而摄动仍为紧摄动时较[1]中更强的结果。 相似文献
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Properties of composition operators induced by analytic self-maps on the unit disk of the complex plane in Hardy-Orlicz spaces are discussed. Results are concerned about boundedness, invertibility, compactness, Fredholm operators and spectra of composition operators. 相似文献
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Art M. Duval Victor Reiner 《Transactions of the American Mathematical Society》2002,354(11):4313-4344
We show that the combinatorial Laplace operators associated to the boundary maps in a shifted simplicial complex have all integer spectra. We give a simple combinatorial interpretation for the spectra in terms of vertex degree sequences, generalizing a theorem of Merris for graphs.
We also conjecture a majorization inequality for the spectra of these Laplace operators in an arbitrary simplicial complex, with equality achieved if and only if the complex is shifted. This generalizes a conjecture of Grone and Merris for graphs.
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Marianna A. Shubov 《Mathematische Nachrichten》2002,241(1):125-162
We develop spectral and asymptotic analysis for a class of nonselfadjoint operators which are the dynamics generators for the systems governed by the equations of the spatially nonhomogeneous Timoshenko beam model with a 2–parameter family of dissipative boundary conditions. Our results split into two groups. We prove asymptotic formulas for the spectra of the aforementioned operators (the spectrum of each operator consists of two branches of discrete complex eigenvalues and each branch has only two points of accumulation: +∞ and —∞), and for their generalized eigenvectors. Our second main result is the fact that these operators are Riesz spectral. To obtain this result, we prove that the systems of generalized eigenvectors form Riesz bases in the corresponding energy spaces. We also obtain the asymptotics of the spectra and the eigenfunctions for the nonselfadjoint polynomial operator pencils associated with these operators. The pencil asymptotics are essential for the proofs of the spectral results for the aforementioned dynamics generators. 相似文献
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Bergman空间上Toeplitz算子的局部及Fredholm性质 总被引:1,自引:0,他引:1
本文讨论了Bergman空间上Toeplitz算子的局部谱的关系.利用局部化原理给出了Toeplitz算子拟换位子紧性的一个充分条件.给出了一类符号的Toeplitz算子是Fredholm算子的充分条件. 相似文献
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The composition operators with closed rangc on H2(B
n) are characterized, and the Fredholmness of products of Toeplitz and composition operators discussed. Moreover, using composition
operators, the spectra of Toeplitz operators are studied.
Project supported by the National Natural Sciencc Foundation of China and the Postdoctoral Science Foundation of China. 相似文献
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In this paper we characterize the essential spectra of Toeplitz operators on Bergman spaces by using Douglas‘ localization Theorem and obtain the local decomposition of the essential spectra of Toeplitz operators. 相似文献
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Sungeun Jung 《Journal of Mathematical Analysis and Applications》2011,384(2):252-260
In this paper we prove that a complex symmetric operator with property (δ) is subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. We also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints. 相似文献
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本文研究了形如∑_n~k=o~((α_k)(e~((α_k)x))D~k(a_k≤0)及∑_k~n=o((-1)~k)α_(2k)D~ke~(α_(2k)x)D~k+i/2∑_k~n=o(α_(2k+1))(D~ke~((α_(2k+1))x)D~(k+1)+D~(k+1)e~((α_(2k+1)x)D~k)(α_k≤0)的算式的谱问题,分别得到了它们的本质谱或本质谱所在的范围. 相似文献