交互作用Fock空间l2(Γ,{λn})上的梯度算子和散度算子

主要研究基于l2(N)上交互作用Fock空间l2(Γ,{λn})中的梯度算子和散度算子.首先定义交互作用Fock空间l2(Γ,{λn})上的梯度算子和散度算子;然后研究梯度、散度算子所具有的算子性质;最后研究由梯度算子和散度算子构成的复合算子与该空间中其他算子的关系.结果表明:交互作用Fock空间l2(Γ,{λn})中的梯度算子和散度算子是稠定线性闭算子,而且它们互为共轭算子,另外,由于该空间中交互因子的特殊性,可得到在l2(Γ,{λn})的n-粒子空间中,梯度、散度算子所构成的复合算子和计数算子相等.     

带紧扰动的极大单调算子的广义度理论及其应用

本文借助于Lerar－Schauder度理论构造了带紧扰动的极大单调算子的广义度，扩展了李树杰与冯德兴相应的结果．运用新的度理论给出了某些算子方程可解性的简单证明．     

加权移位算子是次正常算子的条件

以广义逆为工具运用算子演算给出加权移位算子是次正常算子的条件,所用方法不同于 Ｓｔａｍｐｆｌｉ的工作,但结果一致．作为应用给出了两个例子．     

广义W-Bernstein-Kantorovich算子的构造、收敛性及其渐近表示

运用Kantorovich型算子的构造方法,将一种新的基本Kantorovich算子与广义W-Bern-stein算子复合得到一种新的广义W-Bernstein-Kantorovich算子,证明了它的收敛性并给出了它的Mamedov渐近表达式．     

关于广义Sublaplacian算子特征函数的展开

本文研究了广义Ｓｕｂｌａｐｌａｃｉａｎ算子特征函数的展开．通过定义广义　－扭曲卷积，我们得到相应的Ｐｌａｎｃｈｅｒｅｌ定理及Ｈａｕｓｄｏｒｆｆ－Ｙｏｕｎｇ不等式，最后，我们还给出了当广义Ｓｕｂｌａｐｌａｃｉａｎ算子的特征值为离散时的一些结果．     

相伴于非散度型椭圆算子的Riesz变换的L~p有界性

本文利用小波方法在一般阶的非散度椭圆算子的系数BMO模非常小的情形下,证明了广义 Riesz变换的 L~p(2≤p<+∞)有界性。     

P耗散算子的研究

本文利用广义半内积空间及广义不定度规空间,解决Ｂａｎａｃｈ空间中Ｐ耗散算子的极大耗散扩张表示,并得到很有意义的应用．     

二步幂零Lie群上sub-Laplace算子的谱

本文首先研究包括Ｇｒｅｉｎｅｒ算子和二步幂零Ｌｉｅ群上ｓｕｂ Ｌａｐｌａｃｅ算子Ｌ在内的广义齐次线性偏微分算子的谱，然后利用酉表示理论确定了算子Ｌ的谱结构，并深化了Ｋ．Ｆｕｒｕｔａｎｉ，Ｋ．Ｓａｇａｍｉ，Ｎ．Ｏｔｓｕｋｉ关于Ｌａｐｌａｃｅ算子的有关结果．     

次线性算子在一类广义Morrey空间上的有界性及其应用

证明了一组次线性算子及其交换子,如具有粗糙核的Calderón-Zygmund算子、Ricci-Stein振荡奇异积分、Marcinkiewicz积分、分数次积分和振荡分数次积分及其交换子,在一类广义Morrey空间上的有界性.作为应用得到了非散度型椭圆方程在上述Morrey空间的内部正则性.     

一类解析算子函数空间上的复合算子

本文用算子函数论的方法，研究了解析算子函数的Banach空间X，X0上的复合算子．给出此复合算子为有界的条件，并刻划了此复合算子在X0上为紧的特征．     

Fixed points of generalized e-concave (generalized e-convex) operators and their applications

In this paper, we present the definitions of generalized e-concave operators and generalized e-convex operators, which are the generalizations of e-concave operators and e-convex operators, respectively. Without compactness or continuity assumption of generalized e-concave operators and generalized e-convex operators, we have proved the existence, uniqueness and monotone iterative techniques of their fixed points. Our results are even new to e-concave operators and e-convex operators. Finally, we apply the results to the singular boundary value problems for second order differential equations.     

Generalized random linear operators on a Hilbert space

In this paper, we are concerned with generalized random linear operators on a separable Hilbert space. Generalized random linear bounded operators, generalized random linear normal operators and generalized random linear self-adjoint operators are defined and investigated. The spectral theorems for generalized random linear normal operators and generalized random linear self-adjoint operators are obtained.     

Generalized weighted Morrey spaces and classical operators

We introduce the notion of generalized weighted Morrey spaces and investigate the boundedness of some operators in these spaces, such as the Hardy–Littlewood maximal operator, generalized fractional maximal operators, generalized fractional integral operators, and singular integral operators. We also study their boundedness in the vector‐valued setting.     

Banach空间中闭线性算子广义预解式存在定理

在Banach空间中研究闭线性算子广义逆扰动问题和广义预解式存在性问题.给出了闭线性算子广义逆在T-有界扰动下的一些稳定特征,这些特征推广了在有界线性算子情形、闭线性算子有界扰动情形以及闭线性算子保值域或保核空间情形的一些已知结果.以此为基础,得到了闭线性算子广义预解式存在的一些充要条件及其广义预解式的显式表达式.作为应用,给出了闭Fredholm算子和闭半-Fredholm算子的广义预解式存在性特征.     

On invertible contractions of quotients generated by a differential expression and by a nonnegative operator function

In the present paper, we describe invertible contractions of the maximal quotient generated by a differential expression with bounded operator coefficients and by a nonnegative operator function. We show that the operators inverse to such contractions are integral operators and prove a criterion for such operators to be holomorphic. Using the results obtained, we describe the generalized resolvents of symmetric quotients.     

GENERALIZED OPERATORS AND P（φ）2 QUANTUM FIELDS

In this paper by Sobolev imbedding theorem and characterization theorem of generalized operators the existence of P(φ)2 quantum fields as generalized operators is obtained and a rigorous mathematical interpretation of renormalization procedure is given under white noise theory.     

离散交换群上Toeplitz 算子的代数性质

广泛的意义下定义 Toeplitz 算子, 给出了Toeplitz 算子乘积仍为Toeplitz 算子的充分必要条件, Toeplitz算子是正规算子的充分必要条件以及 Toeplitz 算子可交换的一个必要条件,从而推广了经典 Toeplitz 算子的相应结果.     

On the Approximation of Bounded Functions with Discontinuities of the First Kind by Generalized Shepard Operators

The authors investigate the approximation of bounded functions with discontinuities of the first kind by generalized Shepard operators. Estimate for the rate of convergence at a continuity point is obtained, while at the points of discontinuity it is shown that the sequence of generalized Shepard operators is almost always divergent. It is also shown that the sequence of Cesàro means of generalized Shepard operators is convergent everywhere for bounded functions which have only discontinuities of the first kind in [0,1].     

Banach空间中极大单调算子零点的投影算法

本文设计了一种极大单调算子零点的带误差项的新投影迭代算法,并在Banach空间中,利用Lyapunov泛函与广义投影映射等技巧,证明了迭代序列强收敛于极大单调算子零点的结论.     

ON THE GENERALIZED RESOLVENT OF LINEAR PENCILS IN BANACH SPACES

Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T λ S are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area.