GENERALIZED EXPANSIONS IN HILBERT SPACE

1991MRSubjectClassification35L65.In1957,HllaLu.-K.,,[1]proposedanewapproachtogeneralizedfllnctiolis.Hecollsiclcredf'orulalFourierseriesZaneni:r;isperiodicgelittralizedf'ullcti()llholliatteritisconversantornot.Inthepreselltpaper,wegiveadefinitemeaningoftheseri(lsaboveandgeneralizeit.to;tll;ti)stractHilbertal)ac~.Thedweapl)lyittosol-lienollstrictlyhyl)erbolicsystelll.1GeneralizedExpansionsWithHermitePolynomials1.1Generalizedtrigonometricalseriesyiaretrigonoltletricalpolyllolilials,thenf(J…     

一般度量空间中Boutroux—Cartan定理

本文抓住Ｂｏｕｔｒｏｕｘ－Ｃａｒｔａｎ定理中关键；用到列与圆，将这个定理推广到一般度量空间上去，然后取一些不同的度量空间得出一序列的结果。     

Sobolev空间中的测不准函数

在齐民友[2]的基础上，本文分三种情形讨论了在Sobolev框架下测不准函数的性质：（Ⅰ）H^s-H^-s,(Ⅱ)H^s-H^s,(Ⅲ)Hloc^s-Hcomp^-s.利用Hermite函数作为L^2的正交基底来分解L^2-函数，并引入基本的拟微分算子将H^s-函数化为L^2-函数，本文得到与[2]相似的框架和结果．     

Loewner空间上的拟共形映照

本文把Rn空间上拟共形映照的距离、模、分析定义推广到Loewner空间上,并证明了它们的等价性.     

Loewner空间上的拟共形映照

本文把Ｒｎ空间上拟共形映照的距离、模、分析定义推广到Ｌｏｅｗｎｅｒ空间上，并证明了它们的等价性     

在Hilbert空间与可分Banach空间关于随机级数的收缩原理

在Ｈｉｌｂｅｒｔ空间与可分Ｂａｎａｃｈ空间，用独立随机元收敛准则或三级数定理的思想，证明了关于随机级数的民上缩原理。     

Menger概率n-度量空间中的不动点定理

引进了概率ｎ－度量空间,并将文「１」、「２」的某些主要结果拓广至Ｍｅｎｇｅｒ概率ｎ－度量空间。     

REVERSIBLE MARKOV PROCESSES IN ABSTRACT SPACE

Let \[(E,{\cal E})\] be a measurable space and every single point set {x} belong to \[(E,{\cal E})\].\[q(x) - q(x,A)(x \in E,A \in {\cal E})\]is said to be a q-pair, if (i) For fixed i，q(°), Л)\[A,q(),q(,A)\] is a \[{\cal E}\]-measurable function of x; (ii) For fixed \[x,q(x, \cdot )\] is a measure on \[{\cal E}\], and \[\begin{array}{l} 0 \le q(x,A) \le q(x,E) \le q(x) < \infty .(\forall x \in E,\forall A \in {\cal E})\q(x,\{ x\} ) = 0,(\forall x \in E) \end{array}\] A q-pair of furiotions q (x)- q (x,A) is called conservative when \[q(x,E) = q(x),(\forall x \in E)\]. \[{P_t}(x,A)(t \ge 0,x \in E,A \in {\cal E})\] is said to be a q-process, if (i) For fixed t, A, \[{P_t}(x,A)\] is a \[{\cal E}\]-measnrable function of x; (ii)For fixed t,x, \[{P_t}(x, \cdot )\] is a measure on ê\[{\cal E}\] and \[0 \le {P_t}(x,E) \le 1\]; (iii) \[{P_{s + t}}(x,A) = \int_E {{P_t}} (x,dy){P_s}(y,A),{\kern 1pt} {\kern 1pt} {\kern 1pt} (x \in E,A \in {\cal E},t,s \ge 0)\] (iv)\[\mathop {\lim }\limits_{t \to {0^ + }} \frac{{{P_t}(x,A) - {I_A}(x)}}{t} = q(x,A) - q(x){I_A}(x)(\forall x \in E,\forall A \in {\cal E})\] It is called honest when \[{P_t}(x,E) = 1,{\kern 1pt} {\kern 1pt} {\kern 1pt} (\forall t \ge 0,\forall x \in E)\] A q-process \[{{P_t}(x,A)}\] is called reversible, if there is a probability measure \[\mu \] on \[{\cal E}\] such, that \[\int_A {\mu (dx){P_t}} (x,B) = \int_B {\mu (dx){P_t}} (x,A){\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (\forall t \ge 0.\forall A,B \in {\cal E})\] In this paper, we obtain some oriterions for (i)The existence of a reversible q-process;. (ii)The existence of a honest reversible q-process； (iii)The uniqueness of reversible q-process when the q-pair is conservative.     

ON THE CONNECTION IN FINSLER SPACE

A simple derivation of the Connection in Finsler space.     

简化原理在Hilbert空间与可分Banach空间的一些应用

本文研究了简化原理在Hilbert空间与可分Banach空间中的一些应用,利用简化原理和独立随机元收敛准则获得了中分Banach空间随机级数的收缩原理和B-值随机Dirichlet级数简单收敛横坐标及一般随机整函数的增长性和值分布,将许多以Rademacher序列为系数的随机Tayor级数和随机Dirichlet级数的相关结果,推广到一般的具有独立对称分布系数的随机级数上去。     

快变量空间中的同宿轨道分支

本文考虑奇摄动问题的位于快变量空间中的奇异同宿轨道的保存和周期轨道分支问题文中关于奇异同宿轨道保存的结论推广了一些已知的结果,而周期轨道产生于奇异同宿轨道的分支则提供了一种新的分支类型     

鞅空间理论的新进展

本文是一篇综述性的文字,内容主要是近年来有关鞅空间理论的发展状况,特别是集中于B-值鞅和弱型鞅空间两个部分,可以看做是整个鞅空间理论发展的一个侧面.希望以此引起读者对鞅论的了解和进一步研究的兴趣.具体内容分为以下三节:1.研究鞅空间理论的意义,阐述鞅空间理论与调和分析的关系;2.鞅空间理论的向量值化,阐述B-值鞅不等式与Banach空间几何学的相互依存关系;3.弱型鞅空间与变指数鞅空间的不等式及其应用.     

ADAPTIVITY IN SPACE AND TIME FOR MAGNETOQUASISTATICS

This paper addresses fully space-time adaptive magnetic field computations. We describe an adaptive Whitney finite element method for solving the magnetoquasistatic formulation of Maxwell＇s equations on unstructured 3D tetrahedral grids. Spatial mesh re- finement and coarsening are based on hierarchical error estimators especially designed for combining tetrahedral H（curl）-conforming edge elements in space with linearly implicit Rosenbrock methods in time. An embedding technique is applied to get efficiency in time through variable time steps. Finally, we present numerical results for the magnetic recording write head benchmark problem proposed by the Storage Research Consortium in Japan.     

ON SPACELIKE AUSTERE SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACE

In this article, we construct some spacelike austere submanifolds in pseduoEuclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere submanifolds in pseduo-Euclidean spaces.     

伪黎曼空间型中的2-调和类空子流形

本文研究了伪黎曼空间型中2-调和类空子流形的有关性质.利用活动标架法和Hopf原理,证明了伪脐2-调和类空子流形Mn是极大的,以及如果Mn是紧致的,那么Mn是全测地的,从而推广了[5,7]中的结果.     

THE CHARACTERISTICS OF HYPERSPHERES IN MINKOWSKI SPACE

Y-Riemannian metric gY is an important tool in Finsler geometry, where Y is a smooth non-zero vector field on Finsler manifold. If Y is a geodesic field, it is very effective to study flag curvature using Y-Riemann metric. In this paper, using a special Y-Riemann metric ( that is, so called v-Riemann metric ), we study hyperspheres in a Minkowski space and give some characteristics of hyperspheres in a Minkowski space.     

LINEAR DILATATION OF QUASIREGULAR MAPPINGS IN SPACE

1 IntroductionIn this paPert we use the fOlowing notatioll for Euclidean n-space m and r = Rn U {oo}.Unit vectors in the directions of the rectangular coordinate axes in m are denoted by e1,', en.The open ball and sphere with center x and radius r > 0 are written as B"(x, r) and S"--'(x, r),respectively. We sometimes write Bn (r) = Bn (0, r), S"--'(r) = Sn-- 1 (0, r), Bn = B"(1), Sn-- 1 =sn-- '(1).Let f be a discrete and open maPping from a domain G of R" into R". Thenis called the l…     

NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS IN C SPACE

1IntroductionItiswellknownthatifsupr(t)=r1相似文献   

WEIGHTED BEST LOCAL APPROXIMATION IN ORLICZ SPACE

We present a common fixed point theorem for generalized asymptotically non- expansive and noncommuting mappings in normed linear spaces.