共查询到19条相似文献,搜索用时 125 毫秒
1.
基于C正则预解算子族和双连续C_0半群引入了双连续C正则预解算子族的概念,考察了双连续C正则预解算子族生成元与预解式之间的关系,给出了双连续C正则预解算子族Hille-Yosida型生成定理,从而对Bananch空间强连续半群的生成定理进行了推广. 相似文献
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主要运用Laplace-Stieltjes的方法,讨论Hilbert空间上α-次预解算子族的依范连续性与其预解式的关系,得到一个主要结果:Hilbert空间上α-次预解算子族的依范连续性与其预解式在当|τ|→∞时,‖(ω+iτ)~(α-1)R((ω+iτ)~α,A)‖→0等价. 相似文献
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本文研究了C-正则预解算子族的Abel遍历性和Cesaro遍历性.给出了两种遍历性的 相互关系及其基本性质. 相似文献
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张寄洲 《数学物理学报(A辑)》1997,17(3):294-300
该文研究正则余弦算子函数的内插和外插.证明了线性算子A在Banach空间X中生成一个指数有界的C-正则余弦函数当且仅当存在Banach空间Y和线性算子B使得:[R这里是C在Y中的有界扩张,B在Y中生成一个强连续余弦算子函数且A=B|x. 相似文献
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抽象Cauchy问题的适定性与算子半群 总被引:2,自引:0,他引:2
在算子A非稠定、问题解非指数有界的情况下,研究抽象Cauchy问题的适定性及其与A生成的算子族之间的关系.首先,引进(ACP1)的C适定性概念和C半群生成元的全新定义,证明:(ACP1)是C适定的充要条件是A生成C半群.并给出A生成非指数有界C半群的充分条件.另外,引进(ACP2)的(n,k)适定性定义,并讨论(n,k)适定性与积分余弦函数的关系. 相似文献
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指数有界的C余弦算子函数 总被引:8,自引:0,他引:8
本文引入了指数有界的C余弦算子函数的生成元,讨论了生成元的基本性质,建立了相应的生成定理、逼近定理及扰动定理.最后给出了指数有界的C余弦算子函数与指数有界的C半群的基本联系. 相似文献
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本文提出并研究了Banach空间中的一类新的广义集值变分包含问题:0∈N(ω,y)+A(z,v),由集值m-增生映射的预解算子建立了广义集值变分包含与不动点问题的等价性,并利用Nadler定理和辅助序列建立了一些迭代算法,证明了解的存在性和算法的全局收敛性. 相似文献
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Let \( k \in C(R^+)\), A be a closed linear densely defined operator in the Banach space \(X\) and \( \{R(t)\}_{t\geq 0} \) be an exponentially bounded \(k\)-regularized resolvent operator families generated by A. In this paper, we mainly study pseudo k-resolvent and duality theory of k-regularized resolvent operator families. The conditions that pseudo k-resolvent become k-resolvent of the closed linear densely defined operator A are given. The some relations between the duality of the regularized resolvent operator families and the generator A are gotten. In addition, the corresponding results of duality of \(k\)-regularized resolvent operator families in Favard space are educed. 相似文献
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艾尼·吾甫尔 《应用泛函分析学报》2004,6(2):106-121
首先运用Phillips定理和Fattorini定理证明M/M^k,^B/1排队模型概率瞬态解的存在唯一性,然后通过研究对应于M/M^k,^B/1排队模型的主算子的共轭算子的豫解集得到该主算子的豫解集:在虚轴上除了零点外其它所有点都属于该主算子的豫解集. 相似文献
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This article is concerned with the ill-posed Cauchy problem associated with a densely defined linear operator A in a Banach space. A family of weak regularizing operators is introduced. If the spectrum of A is contained in a sector of right-half complex plane and its resolvent is polynomially bounded, the weak regularization for such ill-posed Cauchy problem can be shown by using the quasi-reversibility method and regularized semigroups. Finally, an example is given. 相似文献
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文章研究有界线性算子半群的扰动问题 .在一定条件下 ,我们表明 :设算子 B生成最终依范连续半群 S(t) (t τ) ,K是有界线性算子 .如果‖ K R(σ+iτ,B) K‖→ 0 ,τ→∞ ,那么算子 A =B +K生成的半群 T(t) ,t>2τ是依范连续的 .我们将此结果应用于迁移算子 ,给出 J rgens结果的一个新证明 . 相似文献
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Let B be a Banach space with norm ‖ · ‖ and identity operator I. We prove that, for a bounded linear operator T in B, the strong Kreiss resolvent condition implies the uniform Kreiss resolvent condition We establish that an operator T satisfies the uniform Kreiss resolvent condition if and only if so does the operator T m for each integer m ? 2.
相似文献
$\parallel (T - \lambda I)^{ - k} \parallel \leqslant \frac{M}{{(|\lambda | - 1)^k }}, |\lambda | > 1,k = 1,2, \ldots ,$
$\left\| {\sum\limits_{k = 0}^n {\frac{{T^k }}{{\lambda ^{k + 1} }}} } \right\| \leqslant \frac{L}{{|\lambda | - 1}}, |\lambda | > 1, n = 0,1,2, \ldots .$
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V. Zh. Sakbaev 《Computational Mathematics and Mathematical Physics》2006,46(4):651-665
The Cauchy problem for the Schrödinger equation with an operator degenerating on a half-line and a family of regularized Cauchy problems with uniformly elliptic operators, whose solutions approximate the solution to the degenerate problem, are considered. A set-valued mapping is investigated that takes a bounded operator to a set of partial limits of values of its quadratic form on solutions of the regularized problems when the regularization parameter tends to zero. The dynamics of quantum states are determined by applying an averaging procedure to the set-valued mapping. 相似文献
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Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space 下载免费PDF全文
Lixin Sheng Weimin Hu You-Hui Su Yongzhen Yun 《Journal of Nonlinear Modeling and Analysis》2024,6(1):194-209
In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii''s fixed point theorem, the theory of evolution family and the resolvent operator. In particular,the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results. 相似文献
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1 IntroductionLet Cbe the open complex plane,let X be a complex Banach space.The set of allbounded linear operators from X into X is denoted by B[X] which is also a Banach space.If X=Cn,the n-dimensional Euclidean space,then B[X] is the set of all n×n matrices,denoted by Cn,n. We denote the spectrum of an operator T∈ B[X] byσ( T) and its resol-vent operator R( λ,T) =( λI-T) - 1 ,where I is the identity operator andλ∈C.The spectral radius of T is denoted by r( T) .N( T) and… 相似文献
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The paper contains formulas for regularized traces of the Laplace-Beltrami operator on the unit sphere under perturbation
determined by a bounded complex-valued potential and a sufficiently complete justification of these formulas.
Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 702–705, May, 2000. 相似文献