预解式

研究了Hilbert空间中的一类广义非线性变分不等式组，运用η次微分算子的预解式技术和辅助原理技术，证明了广义非线性变分不等式组解的存在性和唯一性。

The author studied a new system of generalized nonlinear variational inequalities in Hilbert space . Using the resolvent operator technique of η - subdifferential operator and auxiliary principle , the existence and uniqueness theorem of solution for this kind of system of generalized nonlinear variational inequalities is got .

利用预解式算子技巧构造了一类求变分包含逼近解的迭代算法，并讨论了由此算法产生的迭代序列的收敛性。

By using the resolvent operator technique , a new algorithm for approximating the solution of this class of variational inclusions was given , the convergence of the sequence of iterates generated by the algorithm was also discussed .

构造Banach空间上非线性方程解的预解式迭代过程

Resolvent iteration processes for constructing a solution of a nonlinear equation in Banach space

特别是在Hilbert空间中，可分别用预解式在虚轴上的一致平方可积性和一致有界性刻画系统的小时滞鲁棒稳定性，并很容易得到已有的一些结论。

Specially , in Hilbert spaces , some necessary and sufficient conditions are given in terms of the uniformly square integrability and uniform boundness of the resolvent on the imaginary axis respectively .

在Mann的迭代算法基础上，通过引入算子的预解式，将Hilbert空间中求算子的零点问题转化为解算子不动点问题；

Based on Mann iteration method , the problem of solving zero points of the operator is converted into the one of solving its fixed points by introducing its resolvent in Hilbert spaces .

本文研究Hilbert空间上最终范数连续半群的特征条件，仅利用半群生成元的预解式，给出Hilbert空间上C0-半群最终范数连续的一个的充要条件。

In this paper , a new characterization of eventually norm continuous semigroups on Hilbert space is given . By using the resolvent of the generator , we give the sufficient and necessary conditions for the semigroups to be being eventually norm continuous .

二阶偏算子的共轭算子及预解式

The adjoint and resolvent of a second order partial differential operator

μ-不变测度的Q-预解式刻划

Determination of μ - invariant measure from the q-resolvent function

关于双参数半群的预解式（2）（英文）

On the Resolvent of the Two-parameter Semigroup ( 2 )

一般线性阻尼系统的预解式以及模态正交性

The Resolvents and Modal Orthogonality of General Linear Damped Systems

算子的局部预解式方法及其应用

The Local Resolvent Method for Operators and Its Applications

通过研究双连续C-半群的性质，生成元及其C-预解式之间的关系，得到了双连续C-半群的两个重要定理：生成定理和逼近定理。

Then we conclude two important theorems of bi-continuous C-semigroups : generation theorem and approximation theorem .

本文研究局部预解式方法在算子理论中的应用。

In this paper , the applications of the local resolvent method in the operator theory are studied .

利用新的预解式算子技巧得出一系列广义集值拟变分包含问题的逼近解。

Using the new resolvent operator technique , we obtain the approximate solution for a system of set-valued quasi-variational inclusions .

在§3中，讨论了一类特殊的算子局部预解式的有界性与解析性的关系。

In § 3 , the relationship between the boundedness and the analyticity for a special class of operators is discussed .

在§2中，利用局部预解式方法证明了自对偶次正常算子必有非平凡的不变子空间。

In § 2 , the existence of non-trivial invariant subspaces for a self-dual subnormal operators is proved by means of the local resolvent method .

运用η-次微分算子的预解式技术和辅助原理技术给出了&类似变分不等式问题解的存在性和唯一性。

Using techniques of resolvent formula of η - subdifferential operators and auxiliary principle , we presented the existence and uniqueness of the solution of a class of variational inequalities .

介绍了积分半群及积分半群的解析族，阐述了积分半群的无穷小生成元解析、积分半群解析和预解式解析三者之间的关系。

The paper introduces integrated semi-groups and analytic families of integrated semi-groups , the relations among the three natural ways to understand " analyticity " of the family are clarified .