Invariant Sets in Banach Lattices and Linear Differential Equations and Delay

In this paper we characterize the invariance of some sets with respect to a C ₀-semigroup in Banach lattice. An application to a linear differential equation with delay is given.     

线性算子双半群及在间断和脉冲微分方程中的应用(英)

研究抽象Ｂａｎａｃｈ空间中线性微微分方程的可解性,利用算子双半群方法,讨论了在确定时间跳跃或脉冲的线性微分方程解的存在性,表明在一定条件下间断或脉冲方程的解存在唯一．     

具有内部奇异点的实系数微分算子的自共轭域

研究了一类带有内部奇异点的实系数微分算子自共轭域的描述问题.通过构造相应的直和空间,应用直和空间的相关理论及对相应最大算子域进行分解,在直和空间上生成的相应最小算子具有实正则型域的情形下,利用微分方程的实参数解给出此类算子的自共轭域的完全解析描述,并且确定其边界条件的矩阵仅由微分方程的解在正则点的初始值决定.     

A note on approximation of semigroups of contractions on Hilbert spaces

We show that every contractive C ₀-semigroup on a separable, infinite-dimensional Hilbert space X can be approximated by unitary C ₀-groups in the weak operator topology uniformly on compact subsets of ℝ₊. As a consequence we get a new characterization of a bounded H ^∞-calculus for the negatives of generators of bounded holomorphic semigroups. Applications of our results to the study of a topological structure of the set of (almost) weakly stable contractive C ₀-semigroups on X are also discussed. The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW grant Nr. N201384834.     

Strongly Singular Integral Operators on Weighted Hardy Space

In this paper, we obtain that a strongly singular integral operator is bounded on space for 1 < p < ∞. We also obtain that a strongly singular integral operator is a bounded operator from to for some weight w and 0 < p ≤ 1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on for some w and 0 < p ≤ 1. Supported by National 973 Program of China (Grant No. 19990751)     

Difference estimates for continuous and discrete operator semigroups

For suitable bounded operator semigroups (e ^tA ) _t≥0 in a Banach space, we characterize the estimate ‖Ae ^tA ‖≤c/F(t) for large t, where F is a function satisfying a sublinear growth condition. The characterizations are by holomorphy estimates on the semigroup, and by estimates on powers of the resolvent. We give similar characterizations of the difference estimate ‖T ⁿ −T ⁿ⁺¹‖≤c/F(n) for a power-bounded linear operator T, when F(n) grows faster than n ^1/2 for large n.     

On the Deficiency Indices of Singular Differential Operators in the Degenerate Case

Mathematical Notes -     

Some Solutions for a Class of Singular Equations

In this paper we obtain all solutions which depend only on r for a class of partial differential equations of higher order with singular coefficients.     

微分方程奇点指数的几何计算法

本文提供一种简单的计算奇点指数的方法，文中的结论和例子说明了新方法在计算微分方程指数方面的简洁性     

二阶拟线性方程边值问题的奇摄动

本文借助不动点原理 ,对二阶拟线性方程的边值问题的渐近解做了估计 ,得到了包括边界层在内的任意次近似的一致有效的渐近展开式     

Positive Solutions to Second Order Singular Differential Equations Involving the One-Dimensional M-Laplace Operator

We consider a class of second order quasilinear differential equations with singular ninlinearities. Our main purpose is to investigate in detail the asymptotic behavior of their solutions defined on a positive half-line. The set of all possible positive solutions is classified into five types according to their asymptotic behavior near infinity, and sharp conditions are established for the existence of solutions belonging to each of the classified types.     

利用微积分算子求幂级数的和函数

针对幂级数求和函数的问题,引入借助微分算子、积分算子和微分方程进行计算的方法,可作为逐项微分法和逐项积分法的一种补充．实例说明其应用．     

Graded Differential Equations and Dirac Type Operators

Singularities of solutions of graded differential equations as filtrations are studied. Symbols and the transfer operator associated with the h-adic filtration are computed. The condition that the transfer operator is a differential operator over the characteristic manifold of codimension 1 for this filtration is given. The Dirac operator is introduced by using the De Broglie principle: singularities of wave-like solutions move as material points. Use of the transfer operator associated with the h-adic filtration implies an invariant definition of the Pauli operator. A natural parallel translation arises as quantum analog of the Levi-Civita connection.     

Some Maximal Operators Related to Families of Singular Integral Operators

In this paper, we shall study L^p-boundedness of two kinds of maximal operators related to some families of singular integrals.     

On the Global Solvability of the Cauchy Problem for Singular Functional Differential Equations

Sufficient conditions are found for the global solvability of the weighted Cauchy problem where f : C([a, b]; R ⁿ) L _loc([a, b]; R ⁿ) is a singular Volterra operator, c ₀ R ⁿ, h : [a, b] [0, +] is a function continuous and positive on [a, b], and · is the norm in R ⁿ.     

球壳轴对称弯曲问题精确的挠度微分方程及其奇异摄动解

本文提出了球壳轴对称弯曲问题精确的挠度(ω)微分方程和精确的转角(dω/da)微分方程.本文重点研究了挠度微分方程的精度,基本思路是:首先假设边缘效应时经线中面位移u=0,从而建立挠度微分方程,然后再精确地证明挠度微分方程与原来微分方程内力解答完全相同.再精确地证明边缘效应时经线中面位移u=0是精确解.本文给出了挠度微分方程的奇异摄动解,最后验算了平衡条件,证明摄动解求出的内力和外荷载是完全平衡的.这一方面表明摄动解的计算是正确的;另一方面也再二次表明挠度微分方程是精确的微分方程.新微分方程的优点是:1.新微分方程和原来微分方程精度完全相同;2.新微分方程满足的边界条件非常简单;3.新微分方程便于使用摄动解;4.新微分方程可以得到挠度(ω)和转角(dω/da)的表达式.新微分方程使球壳的计算得到很大的简化.本文采用的符号与徐芝纶《弹性力学》第二版下册相同[1].     

Poisson Equations Associated with Differential Second Quantization Operators in White Noise Analysis

In this paper we shall show the heredity of a differentiable one-parameter semigroup under the second quantization and then discuss the resolvent of the differential second quantization operator and the potentials of test white noise functionals. As an application, we shall investigate the existence of solutions of the Poisson-type equations associated with differential second quantization operators as well as operators similar to differential second quantization operators.     

Well-posedness of linear partial differential equations with unbounded delay operators

In this paper we show the well-posedness of the following constant delay equation: