Krein空间上J-正常算子的可定化性

对于Krein空间上J-正常算子 的各种可定化性进行了研究. 利用可定化J-正常算子的谱函数, 给出了临界线的概念, 得到了可定化的J-正常算子成为强可定化算子和一致可定化算子的充要条件.     

一类非线性算子的不动点定理及其应用

本文利用半序方法讨论了u0凹、-u0凸算子的不动点存在唯一性定理及迭代序列的收敛性问题,还讨论了序凹、序凸算子及u0凸算子的有关问题及它们在Ham- merstein型积分方程中的应用.所得结论推广并改进了已有的相关结论.     

一类增算子不动点定理及其应用

利用锥理论和非对称迭代方法,讨论了不具有连续性和紧性条件的增算子方程解的存在唯一性.作为其应用着重讨论了非增算子方程解的存在唯一性,并给出了迭代序列收敛于解的误差估计,改进和推广了某些已知结果.     

一类二阶二次变系数微分算子的不变子空间及其应用

研究了一类二阶二次变系数微分算子的不变子空间,讨论了这类微分算子不变子空间的应用,并给出了具体应用的一些例子.在这些例子中,构造了大量变系数非线性演化方程的精确解.     

Isomorphic Properties of One Class of Differential Operators and Their Applications

We consider a special class of quasielliptic matrix operators and establish isomorphic properties of these operators in special scales of weighted Sobolev spaces. We give an example of application of these results to systems of differential equations that are not solved with respect to the derivative.     

On a Class of Covariance Operators

This paper is the continuation of [1] in which complex symmetries of distributions and their covariance operators are investigated. Here we also study the most general quaternion symmetries of random vectors. Complete classification theorems on these symmetries are proved in terms of covariance operator spectra.     

On a Class of Integral Operators

In this paper we consider the space where dv _s is the Gaussian probability measure. We give necessary and sufficient conditions for the boundedness of some classes of integral operators on these spaces. These operators are generalizations of the classical Bergman projection operator induced by kernel function of Fock spaces over .      

Definitizability of Certain Functions and the Existence of Eigenvectors of Unitary Operators in Pontrjagin Spaces

Let P_k^c(G) denote the set of continuous functions with k negative squares on a locally compact commutative group G. Every function f ? P_k^c(G) is definitizable in the sense that is positive definite for certain complex measures ω on G with finite support [9]. The proof of this fact was base on a result of M. A. Naimark about common nonpositive eigenvectors of commuting unitary operators in a Pontrjagin space. It is the aim of this note to prove without any use of the theory of Pontrjagin spaces the definitizability of functions f ? P_k^c(G) which are of polynomial growth. In Section 3 we show, how the definitizability of functions f ? P_k^c(G) can be used to prove the existence of common non-positive eigenvectors of commuting unitary operators in a Pontrjagin space.     

一类带不定权函数的奇型Sturm-Liouville算子的局部可定性(英文)

研究一类带不定权函数的奇型Sturm-Liouville算子,给出相应自伴算子在无穷点邻域的局部可定性.     

剩余格上的一类模糊滤算子及其应用

在剩余格上引入了模糊滤算子,讨论了它的一些性质。特别地,将这类算子应用到EQ-代数研究中,给出了格EQ-代数和好的EQ-代数的模糊滤算子刻画,分离的EQ-代数的模糊自同态算子刻画。     

On a Class of Weakly Hyperbolic Operators

The paper considers Cauchy problem in the Gevre type multianisotropic spaces. Necessary and sufficient conditions for unique solvability of this problem are obtained and the properties of operators (polynomials) that are hyperbolic with a specified weight are investigated.     

Tunneling for a Class of Difference Operators

We analyze a general class of difference operators ${H_\varepsilon = T_\varepsilon + V_\varepsilon}$ on ${\ell^2((\varepsilon \mathbb {Z})^d)}$ where ${V_\varepsilon}$ is a multi-well potential and ${\varepsilon}$ is a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for ${H_\varepsilon}$ as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schr?dinger operator [see Helffer and Sj?strand in Commun Partial Differ Equ 9:337–408, 1984], and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.     

A Note on a Class of Operators

The aim of this note is to study the spectral properties of the LUECKE's class R of operators T such that ‖(T – zI)^?1‖=1/d(z, W(T)) for all z?CLW(T), where CLW(T) is the closure of the numerical range W(T) of T and d(z, W(T)) is the distance from z to W(T). The main emphasis is on the investigation of those properties of operators of class R which are either similar to or distinct from those of operators satisfying the growth condition (G₁).     

一类具有转移条件高阶微分算子的J-自伴性

本文研究了一类具有转移条件的高阶复系数微分算子的J-自伴性,利用J-对称微分算式的拉格朗日双线性型、J-自伴算子的定义及矩阵表示的方法,证明了这类微分算子是J-自伴的,且对应于不同特征值的特征向量和特征子空间都是C-正交的.     

Regularity for a Class of Elliptic Operators with Dini Continuous Coefficients

We obtain regularity results for solutions to Pu=f when P is a kth order elliptic differential operator with the property that both P and P ^t have coefficients that are continuous, with a modulus of continuity satisfying a Dini-type condition. Operators of this form arise in the study of regularity of functions that are known to be regular along the leaves of several foliations, such as arise in Anosov systems. The results here complement some previous results of the author and J. Rauch.     

Agmon-Type Estimates for a Class of Difference Operators

We analyze a general class of self-adjoint difference operators , where V _ε is a one-well potential and ε is a small parameter. We construct a Finslerian distance d induced by H _ε and show that short integral curves are geodesics. Then we show that Dirichlet eigenfunctions decay exponentially with a rate controlled by the Finsler distance to the well. This is analog to semiclassical Agmon estimates for Schr?dinger operators. Submitted: February 23, 2008. Accepted: May 23, 2008.     

Complex Symmetry of a Dense Class of Operators

In this paper, we develop new techniques to study complex symmetric operators. We first give an interpolation theorem related to conjugations. This result is used to give a geometric characterization for a norm-dense class of operators to be complex symmetric. Also we characterize certain complex symmetric nilpotent operators, and several illustrating examples are given.     

On a Class of Operators of Finite Type

This paper studies some class of pure operators A with finite rank self-commutators satisfying the condition that there is a finite dimensional subspace containing the image of the self-commutator and invariant with respect to A*. Besides, in this class the spectrum of operator A is covered by the projection of a union of quadrature domains in some Riemann surfaces. In this paper the analytic model, the mosaic and some kernel related to the eigenfunctions are introduced which are the analogue of those objects in the theory of subnormal operators.     

K-理论在一类算子逼近中的应用

构造了一类强不可约的Cowen—Douglas算子,刻画了其换位代数的K_0-群.我们证明了:对于复可分的Hilbert空间上的有界线性算子T及ε0,总可以找到由有限多个强不可约的Cowen-Douglas算子构成的直和算子S,使得||T-S||ε.     

α凸算子(α>1)的正不动点存在性及其应用

通过构造一个特殊的锥,利用锥拉伸与压缩不动点定理对α凸算子(α>1)正不动点的存在性与不可比较性作了研究,并将其结果应用到超线性多项式型Hammerstein积分方程．