对称算子的两种自伴延拓形式之间的联系

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.     

向量值函数空间中J-对称算子的J-自伴延拓

给出了向量值函数空间中J-对称算子的J-自伴延拓的完全解析描述.我们应用Knowles理论,借助方程τ(y)=λ     

Carlemam估计的新方法及其应用

利用一种新的方法,建立了Tnicomi算子的强唯一延拓性.并对具临界位势的Tricomi算子与Schrodinger算子的强唯一延拓性得到了一些肯定性的结果.     

具有对数函数系数的J-自伴微分算子谱是离散的充分条件

运用算子直和分解、Lidskii定理和二次型比较法,研究了一类具有对数函数系数的J-自伴微分算子谱的离散性,得到了这类J-自伴微分算子谱离散的若干充分条件.     

Carlemam估计的新方法及其应用

利用一种新的方法,建立了Ｔｒｉｃｏｍｉ算子的强唯一延拓性．并对具临界位势的Ｔｒｉｃｏｍｉ算子与 Ｓｃｈｒｏｄｉｎｇｅｒ算子的强唯一延拓性得到了一些肯定性的结果．     

有界格上三角子模的一种新的延拓方法

介绍了有界格上￡-子模(余子模)的一种新的延拓方法,同时研究了延拓得到的t-子模(余子模)的一些性质.所得的结果表明这种新的延拓方法是一种好的延拓方法.     

两个四阶微分算子积的自伴性

本文研究由微分算式D^4-DpD q生成的两个四阶微分算子Li(i=1，2)的积L2L1的自伴性，并在常型和奇型情形下，分别获得了两个四阶微分算子积自伴的充要条件．同时证明了若L1和L2自伴，则L=L2L1自伴的充要条件是L1=L2．     

二阶微分算子积的自伴性

本文讨论了由正则和奇异的二阶对称微分算式生成的微分算子的积算子的自伴性,得到了积算子为自伴算子时边条件应满足的充分而必要的条件及若干其他结果．     

极限圆型Hamilton算子乘积的自伴性

本文讨论了极限圆型Hamilton算子乘积的自伴性,利用Calkin方法及奇异Hamilton系统自伴扩张的一般构造理论,给出了在极限圆型时判定Hamilton算子乘积自伴的一个充要条件.     

算子张量积及C_2上的初等算子

本文给出了形如的张量积算子成为自伴算子，Ｃ＿ｐ类算子，有限秩算子及一秩算子的充分必要条件，特别，作为应用，得到Ｈｉｌｂｅｒｔ－Ｓｃｈｍｉｄｔ类Ｃ＿２（Ｈ）上初等算子成为自伴算子，Ｃ＿ｐ类算子的充分必要条件．     

Symmetric anti-eigenvalue and symmetric anti-eigenvector

The idea of symmetric anti-eigenvalue and symmetric anti-eigenvector of a bounded linear operator T on a Hilbert space H is introduced. The structure of symmetric anti-eigenvectors of a self-adjoint and certain classes of normal operators is found in terms of eigenvectors. The Kantorovich inequality for self-adjoint operators and bounds for symmetric anti-eigenvalues for certain classes of normal operators are also discussed.     

对称Fock空间上的加权复合算子

本文研究了可分Hilbert空间上的对称Fock空间上有界(线性和反线性)加权复合算子. 完全刻画了酉加权复合算子和自伴加权复合算子, 并考虑了一类正规加权复合算子.     

辛对称Hamilton算子值域的闭性

利用扰动理论和算子矩阵的因式分解,研究了辛对称Hamilton算子值域的闭性.针对对角占优、上行占优等情形,在一定条件下给出了值域闭性的若干描述,并得到了一般情形的结果.     

Remarks on the Structure of Complex Symmetric Operators

A conjugation C is antilinear isometric involution on a complex Hilbert space , and is called complex symmetric if T* = CTC for some conjugation C. We use multiplicity theory to describe all conjugations commuting with a fixed positive operator. We expand upon a result of Garcia and Putinar to provide a factorization of complex symmetric operators which is based on the polar decomposition. This paper is based in part on the first author’s Master’s Project.     

Hardy空间上一类$m$-复对称Toeplitz算子

本文主要研究Toeplitz算子相对于一对置换的共轭算子是2-复对称的充要条件. 首先在经典的Hardy空间上介绍一类被称为一对置换的共轭算子, 其次完整地刻画了在这类共轭算子下Toeplitz算子是2-复对称的结构, 利用Toeplitz算子在Hardy空间的经典正规正交基下的矩阵表示来刻画2-复对称Toeplitz算子. 最后对于Toeplitz算子分别补充前提$f_n=-f_{-n}$和$f_n=f_{-n}$, 得到了更简化的结果. 在第二个前提下, 研究Toeplitz算子的3-复对称性, 得到$T_f$关于$C_{(i,j)}$是3-CSO的结果和是2-CSO相同.     

The HeatKernel ofthe Sym m etric Space P_n

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｈｅａｔｋｅｒｎｅｌｏｆａｍａｎｉｆｏｒｌｄｃｏｎｔａｉｎｓｒｉｃｈｉｍｆｏｒｍａｔｉｏｎｏｆｇｅｏｍｅｔｒｙａｎｄａｎａｌｙｓｉｓｏｆｔｈｅｍａｎｉｆｏｌｄ．Ｒｅｃｅｎｔｙ，ｍａｎｙｍａｔｈｅｍａｔｉｃｉａｎｓａｎｄｐｈｙｓｉｓｔｓａｒｅｉｎｔｅｒｅｓｔｅｄｉｎｔｈｉｓｆｉｅｌｄａｎｄａｌｏｔｏｆｉｍｐｏｒｔａｎｔｒｅｓｕｌｔｓａｒｅｏｂｔａｉｎｅｄ．ＬｅｔＰｎ（Ｃ）ｄｅｎｏｔｅｔｈｅｓｅｔｏｆａｌｌｎ×ｎｃｏｍｐｌｅｘＨｅｒｍｉｔｅｐｏｓｉｔｉｖｅｄｅｆ…     

有界对称区域上Dirichlet空间中的紧Toeplitz算子

介绍了有界对称区域Ω上Dirichlet空间中的Toeplitz算子的紧性:如果S是有限个Toeplitz算子乘积的有限和,S是紧算子当且仅当S的Berezin变换S(z)趋于0.     

Deficiency Indices of a Symmetric Ordinary Differential Operator with Infinitely Many Degeneration Points

Let H be the minimal symmetric operator in L ²() generated by the differential expression (-1) ⁿ (c(x)f ⁽ⁿ⁾)⁽ⁿ⁾, n 1, with a real coefficient c(x) that has countably many zeros without finite accumulation points and is infinitely smooth at all points x with c(x) 0. We study the value Def H of the deficiency indices of H. It is shown that DefH=+ if infinitely many zeros of c(x) have multiplicities p satisfying the inequality n – 1/2 < p < 2n – 1/2. Our second result pertains to the case in which the set of zeros of c(x) is bounded neither above nor below. Under this condition, Def H = 0 provided that the multiplicity of each zero is greater than or equal to 2n – 1/2. The multiplicities of zeros of c(x) are understood in the paper in a broader sense than in the standard definition.     

Symmetric invariant cocycles on the duals of q-deformations

We prove that for q∈C^? not a nontrivial root of unity any symmetric invariant 2-cocycle for a completion of Uqg is the coboundary of a central element. Equivalently, a Drinfeld twist relating the coproducts on completions of Uqg and Ug is unique up to coboundary of a central element. As an application we show that the spectral triple we defined in an earlier paper for the q-deformation of a simply connected semisimple compact Lie group G does not depend on any choices up to unitary equivalence.