共查询到20条相似文献,搜索用时 15 毫秒
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该文讨论一般非均匀凸介质所确定的迁移算子的广义本征函数系统的完整性问题,利用我们探索的相对收敛方法,完整地刻划了一般非均匀凸介质中迁移问题的广义本征函数系统的完整性问题,我们证明了,对迁移半群E(t),当0∈Pσ(E(t)),迁移算子广义本征函数系统不完整,当0∈Pσ(E(t))时,仅当满足相对收敛条件时,迁移算子的广义本征函数系统完整. 相似文献
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有界线性算子的点谱和剩余谱分别可进-步细分为两类:σ_(p1),σ_(p2)和σ_(r1),σ_(r2).设H,K为无穷维可分的Hilbert空间,本文将对于给定的A ∈B (H),B ∈B(K),给出了缺项算子M_C=(AC/OB)关于分类后所得四种谱的扰动结果. 相似文献
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Let L0 be a 2 × 2 diagonal self‐adjoint block operator matrix with entries A and D. If operators B and B* are added to the off diagonal zeros, certain parts of the spectrum of L0 move to the right and other parts move to the left. In this paper it is shown that, correspondingly, if B is a trace class operator M. G. Krein's spectral shift function is of constant sign on certain intervals. 相似文献
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Let =(A C X B)be a 2×2 operator matrix acting on the Hilbert space н( )κ.For given A ∈B (H),B ∈B(K)and C ∈B(K,H)the set Ux∈B(H,к)σe(Mx)is determined,where σe(T)denotes the essential spectrum. 相似文献
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The eigenfunction expansions of an integer power of the Schrödinger operator in an arbitrary two-dimensional domain are considered. The convergence of the corresponding expansions of piecewise smooth functions is proved. When the dimension of the domain is greater than two, then it is well known that this result is not valid any more. 相似文献
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We consider operator matrices ${\rm{H = }}\left( {{_{B_{10} }^{A{_0}}} {_{A_{1} }^{B{_{01}}}} } \right)$ with self - adjoint entries Ai, i = 0,1, and bounded B10 = B10 acting in the orthogonal sum μ=μ0 ⊕ μ1 of Hilbert spaces μ0 and μ1. We are especially interested in the case where the spectrum of, say, A1 is partly or totally embedded into the continuous spectrum of A0 and the transfer function V1(z) = B10 where (χ - A0)?1 B01, admits analytic continuation (as an operator - valued function) through the cuts along branches of the continuous spectrum of the entry A0 into the unphysical sheet(s) of the spectral parameter plane. The values of χ in the unphysical sheets where M1?1(z) and consequently the resolvent (H - z)?1 have poles are usually called resonances. A main goal of the present work is to find non - selfadjoint operators whose spectra include the resonances as well as to study the completeness and basis properties of the resonance eigenvectors of M1(z) in μ1. To this end we first construct an operator - valued function V1(Y) on the space of operators in μ1 possessing the property: V1(Y)?1 = V1(z)?1 for any eigenvector ?1 of Y corresponding to an eigenvalue z and then study the equation H1 = A1 + V1(H1). We prove the solvability of this equation even in the case where the spectra of A0 and A1 overlap. Using the fact that the root vectors of the solutions H1 are at the same time such vectors for M1(z), we prove completeness and even basis properties for the root vectors (including those for the resonances). 相似文献
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Let r ∈ ? be a complex number, and d ∈ ?≥2 a positive integer greater than or equal to 2. Ashihara and Miyamoto [4] introduced a vertex operator algebra V 𝒥 of central charge dr, whose Griess algebra is isomorphic to the simple Jordan algebra of symmetric matrices of size d. In this article, we prove that the vertex operator algebra V 𝒥 is simple if and only if r is not an integer. Further, in the case that r is an integer (i.e., V 𝒥 is not simple), we give a generator system of the maximal proper ideal I r of the VOA V 𝒥 explicitly. 相似文献
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有理对称矩阵的准正交相似 总被引:1,自引:0,他引:1
滕冬梅 《数学的实践与认识》2011,41(18)
对一个有理对称矩阵A,用线性代数的理论直接证明了存在准正交矩阵P使得P~(-1)AP成为A的有理标准形,并给出了P的算法. 相似文献
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With a view toward the correlation matrices, it is shown that the normalized real symmetric matrices are the affine hull of the binary correlation matrices, while the convex hull is a proper subset of the correlation matrices. A number of ways to identify the correlation matrices in the affine hull are discussed. 相似文献
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With a view toward the correlation matrices, it is shown that the normalized real symmetric matrices are the affine hull of the binary correlation matrices, while the convex hull is a proper subset of the correlation matrices. A number of ways to identify the correlation matrices in the affine hull are discussed. 相似文献
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设A和B为无限维复Banach空间上的标准算子代数,记Δ~R(·)为下列谱函数之一:σ~R(·),σ_l~R(·),σ_r~R(·),σ_l~R(·)∩σ_r~R(·),(?)σ~R(·),(?)σ~R(·),σ_p~R(·),σ_c~R(·),σ_(ap)~R(·),σ_s~R(·),σ_(ap)~R(·)∩σ_s~R(·),σ_p~R(·)∩σ_c~R(·),σ_p~R(·)∪σ_c~R(·),其中R=A或B.证明了A和B之间的每个保持算子Jordan三乘积(算子乘积)之谱函数△~R(·)的满射Φ必有形式Φ=(?)π,其中(?)是1的立方根(1的平方根)而π或者是A和B之间的代数同构,或者是代数反同构.也获得不定度规空间上的标准算子代数之间保持算子斜乘积之谱函数的映射的完全刻画. 相似文献
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考虑了von Neumann形式的自伴延拓和以Calkin方法给出的自伴延拓之间的关系,证明了这两种自伴延拓是一致的并可以互相转化的. 相似文献
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Operator Matrix Forms of Positive Operators 总被引:2,自引:0,他引:2
If a 3-tuple (A:H1→H1,B:H2→H1,C:H2→H2)of operators on Hibert spaces is given,we proved that the operator ~↑A:=(↑A ↓B^*↑B ↓C) on H=H1 H2 is ≥0 is and only if A≥0,R(B)∪→R(A^1/2) and C≥B^* A^ b,where A^ is the generalized inverse of A.In general,A^ is a closed operator,but since R(B)∪→R(A^1/2,B^* A^ B is bounded yet. 相似文献