共查询到19条相似文献,搜索用时 78 毫秒
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在α次积分C半群和双连续n次积分C半群的基础上,探讨了双连续α次积分C半群的扰动性,得到了双连续α次积分C半群的扰动定理,并且在局部Lipschitz连续条件下证明双连续α次积分C半群的扰动理论仍然成立. 相似文献
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一些单叶函数族导数的积分平均值 总被引:1,自引:0,他引:1
K(α),st_k(α),C(β,α),(α<1,β<1)分别表示α阶凸函数族,k 次对称的α阶星形函数族,α型β阶的近于凸函数族.在这篇文章中,我们分別对(?)(K(α)的闭凸包),(?),(?),(α<1,β≤1/2)决定了凸泛函L(f)=(1/(2π)(?)))~(1/p),0≤r<1,p≥1,n=1,2,…,的极值和极值函数.我们的结果表明:极值函数仅依赖于函数族而与参数 n,r,p 无关;而且对任何固定的函数族,除掉旋转外极值函数是唯一的. 相似文献
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闭逐块光滑流形上的Cauchy—Fantanppie型积分的边界性质 总被引:9,自引:0,他引:9
对C^n空间中具有逐块C^(1)光滑可定向边界δD的有界域D和著名的Cauchy-Fantappie公式,本文定义一类与Bochner-martinelli核同伦等价的C-F核Ω,应用同伦方法证明具有Holder密度的相应奇异积分F(t)存在哥西主值和C-F型积分F(z)存在满足Holder条件的内,外极限值F^+(t)和F^-(t);同时建立一个更一般的含有边界上点t的立体角系数α(t)的Ple 相似文献
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本文通过对次调函数基本性质的讨论,对从属函数族建立了积分平均原理,然后给出它在星象函数族与凸象函数族中的运用,解决了面积极值问题和长度极值问题.并给出星相与凸象族以及其导数的积分平均原理,然后推扩到由星象或凸象函数所定义的函数族上去,这一方法还可运用许多其它函数族. 相似文献
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在这篇文章内,研究一类含参数线性一算子族A(t)和线性算子B的积-微分方程,应用积分半群方法证明了该方程存在指数有界解,和含A(t),B的二阶微分方程存在指数有界和分解。这里A(t),B不必满足Hille-Yosida条件。 相似文献
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利用经典算子半群理论中的方法,基于指数有界双参数n阶α次积分C群的概念,得到了指数有界双参数n阶m次积分C群的指数公式 相似文献
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Gao Mingchu 《东北数学》1998,(1)
in this paper, we first give a Hille-Yosida type sufficient and necessary conditionfor n-times integrated mild C-existence families. Then, we present a Laplace type sufficientand necessary condition for exponentially bounded n-times integrated C-semigrougs, andstudy the relationship between integrated regularized semigroups and general regularizedsemigroups. Finally, we offer a characterization of integrated C-semigroups in terms of thesolvability of abstract Cauchy problems. 相似文献
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在α次积分半群的扰动理论的基础上,讨论了α次积分C-半群的可交换扰动问题,得到了α次积分D半群的扰动定理. 相似文献
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α-次积分半群的Trotter-kato定理 总被引:2,自引:0,他引:2
§1. IntroductionWhenweintegratedifferentialequations,wecanformulatemanyofthemasanabstractCauchyproblem.AnaturalquestioninthetheoryistofindsuitableconditionsunderwhichasequenceofaabstractCauchyproblem.u′n=Anun(t),un(0)=xn,fort≥0,n=1,2,…inanarbtiraryBa… 相似文献
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高明杵 《数学物理学报(B辑英文版)》1998,(1)
0IntroductionIn[1],deLaubenfelsdefilledexpollelltiitllyboullded11olonlorphicC-existeuccfalllilies,holomorpllicC-senhgroupsand11olonlorpllicilltegratedselnigroups.Healsodiscussedtheirrelationships,alldgavesomeHille-YOsidatypecollditiollsforalloperatortogenerateallyofthesefamiliesofoperatorsin[1].ZllengalldLetdefinedexpollelltiallyboulldedllololllorphiconceilltegratedC-semigroups,andpreselltedageueratiolltlleorelllill[2J.Moregelleral71-tilllesintegratedmildC-existencefamilieswereintroducedby… 相似文献
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本文中,我们定义了完全二阶抽象柯西问题的温和C-存在族.对指数有界的温和C-存在族,我们还给出了温和C-存在族的Hille-Yosida型的充要条件.对不完全二阶抽象柯西问题,我们定义了解空间和Hille-Yosida空间,我们还证明了不完全二阶抽象柯西问题在其Hille-Yosida空间上是自动适定的,把deLaubenfels文中关于一阶抽象柯西问题的相应结果推广到了二阶的情形. 相似文献
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In 2000,Shi and Feng gave the characteristic conditions for the generation of C0semigroups on a Hilbert space.In this paper,we will extend them to the generation of α-times resolvent operator families.Such characteristic conditions can be applied to show rank-1 perturbation theorem and relatively-bounded perturbation theorem for α-times resolvent operator families. 相似文献
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We establish some left and right multiplicative perturbations of a local α-times integrated C-semigroup S(·) on a complex Banach space X with non-densely defined generator, which can be applied to obtain some additive perturbation results concerning S(·). Some growth conditions of the perturbations of S(·) are also established. 相似文献
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We find the exact small deviation asymptotics for the L2-norm of various m-times integrated Gaussian processes closely connected with the Wiener process and the Ornstein – Uhlenbeck process. Using a general approach from the spectral theory of linear differential operators we obtain the two-term spectral asymptotics of eigenvalues in corresponding boundary value problems. This enables us to improve the recent results from [15] on the small ball asymptotics for a class of m-times integrated Wiener processes. Moreover, the exact small ball asymptotics for the m-times integrated Brownian bridge, the m-times integrated Ornstein – Uhlenbeck process and similar processes appear as relatively simple examples illustrating the developed general theory.Partially supported by grants of RFBR 01-01-00245 and 02-01-01099. 相似文献