Hilbert空间中C_o-半群族指数稳定性

主要讨论了Hilbert空间中Co-半群族Th(t)指数稳定问题,证明了满足||Th(t)||≤Meσt(M,σ与h无关)的半群族Th(t)指数稳定与弱Lp-稳定是等价的,并且给出了另外的三个判定Th(t)指数稳定的等价条件.     

自反Banach空间中C0-半群族的稳定性

主要讨论了自反Banach空间中一类C0-半群族{Th(t)}稳定性问题,证明了此类半群族{Th(t)}指数稳定与弱Lp-稳定是等价的.     

Hilbert空间中算子半群指数稳定的一个问题

设H为复的Hilbert空间,T(t)是H上的(1,A)类算子半群,A为T(t)的无穷小母元。(1.A)类半群T(t)称作指数稳定的,若存在正数M和σ,使对一切t≥1,有 ||T(t)||≤Me~(-σt)。 本文对满足条件∫_0~1||Tt||~2 dt<+∞的(1,A)类半群回答了Pritchard和Zabczyk在[1]中提出的公开问题,证明T(t)指数稳定的充要条件是存在实数p≥1,使对一切x,y∈H,有 ∫_1~(+∞)|(T(t)x,y)|~p dt<+∞。     

L^q（Ω）空间中Co—半群的一些结果

设T（t)是L^q(1＜q＜∞）空间上的Co-半群,A为其元穷小生成元。本文证明若T（t)是弱L^p稳定的,则其生成元的谱界是负的。由Lotz Weis最近得到的关于L^q(Ω）空间中正Co半群的增长界等于生成元的谱界这一结果得出,L^q(Ω）空间中正Co半群弱L^p稳定与与指数稳定等价。     

Earthquake曲线切向量上的范数

本文研究了定义在earthquake曲线切向量上的范数，首先证明了一条earthquake曲线ht上初始切向量的范数等价于earthquake测度σ的Thurston范数．其次证明了当t→∞时，ht的切向量Vt的范数增长渐近等于O(||→||The^Ct||σ||Th)，其中C是正的万有常数，||σ||Th是σ的Thurston范数，而O所代表的常数是渐近万有的，也即当t||σ||Th充分大时它是万有的．此外，附带证明了定义在Zygmund有界函数上的两种交比范数是等价的．     

算子半群母元豫解式的增长阶和它的指数稳定性

设X为Banach空间,T(t)为X上的(1,A)类半群,A为T(t)的无穷小母元,若对每个x∈X,映射t→T(t)x关于t>t_0可微,则称T(t)关于t>t_0可微,本文讨论了关于t>t_0可微的(1,A)类半群的若干性质,并利用可微半群母元豫解式的增长阶特征证明了关于t>t_0可微的(1,A)类半群是指数稳定的充分必要条件为sup{Reλ:λ∈σ(A)}<0.     

关于C_0-半群的谱映象定理的推广

本文讨论了指数函数谱映象定理不成立的实质,分析了C_0-半群e~(At)的谱σ(e~(At))和它的生成元A的谱σ(A)之间的关系。对一类算子A给出了由σ(A)计算e~(At)的谱半径e~(ω0(A)t,t≥0的精确公式。     

退化C_0-半群族的指数稳定性

首先,应用泛函分析和算子理论在Hilbert空间中得到了关于退化C_0-半群指数稳定的充分必要条件.然后,讨论了退化C_0-半群族的指数稳定性问题,应用退化C_0-半群理论给出了充分必要条件.     

Banach空间积分双半群的生成条件

研究Banach空间中积分双半群的生成条件.利用算子A的豫解算子,给出了积分双半群T(t)的生成定理.结果表明:如果对任意的x∈X,f∈X*,以及A|λ]<δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t),t∈R,S(t)强连续且满足积分双半群的定义.     

Lq(Ω)空间中C0-半群的一些结果

设T（t）是Lq（1＜q＜∞）空间上的C0-半群,A为其无穷小生成元．本文证明若T（t）是弱LP稳定的,则其生成元的谱界是负的。由LotzWeis最近得到的关于Lq（Ω）空间中正C0半群的增长界等于生成元的谱界这一结果得出,Lq（Ω）空间中正C0半群弱Lp稳定与指数稳定等价．     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Birational aspects of the geometry of Varieties of Sums of Powers

Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.