一类包含S—闭空间和紧空间的拓扑空间

本文定义了WS—闭空间的概念,它是S—闭空间和紧空间的推广.文中讨论了WS—闭空间的一些性质,推广了s—闭空间的一些结果.     

仿紧局部紧空间的映象

本文借助于闭映射、伪开映射和商映射建立仿紧局部紧空间和几类具有某些特定性质 k 系空间之间的联系。     

L—FUZZY拓扑空间中几种紧性

本文在L－fuzzy拓扑空间中引进了几种不同的具有有限交性质的闭集族，并以此刻划了良紧空间、强F紧空间和F紧空间的特征。另外，对F紧空间还给出了复盖式以及远域族式的刻划。     

关于不可约空间

不可约(irreducible)空间引起人们的兴趣是从1950年Arens-Dugundji利用弱仿紧(metacompact)空间的不可约性证明了“弱仿紧的可数紧(countably compact)空间是紧空间”开始的.以后人们一方面寻找哪些类型的空间具有不可约性,另一方面发现了不可约性的类似于使可数紧性成为紧性的一些作用.这样,就使不可约性在拓扑空间理论中,特别是覆盖性质方面起着很大作用.本文错综地介绍达两方面的结果及一些未解决的问题. 定义1 空间X的开覆盖(?)称为最小的(minimal),如果不存在(?)的其子族覆盖x.空间X称为不可约的,如果X的每一开覆盖具有最小的加细开覆盖.     

集值映射空间在紧开拓扑下的NO性质

本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若X,Y为NO空间,则X到Y上的点紧致的连续集值映射族依紧开拓扑是NO空间,从而将Michael[1]的结论推广到更大的映射空间类上.     

集值映射空间上的■0特征1

应用k-网的概念证明了:若X,Y为■0空间且Y为局部紧的,则X到Y上满足条件(G)的点紧致的族连续集值映射族依紧开拓扑是■0空间.     

集值映射空间在紧开拓扑下的N_0性质

本文讨论了点紧致的连续集值映射空间在赋予紧开拓扑下的某些拓扑性质,证明了:若X,Y为N_0空间,则X到Y上的点紧致的连续集值映射族依紧开拓扑是N_0空间,从而将Michael的结论推广到更大的映射空间类上.     

L-拓扑空间的相对α-紧性

研究了L-拓扑空间的相对α-紧集.基于α-紧性,在L-拓扑空间中引入相对α-紧性的概念,得到了它的一些性质,如它是L-好的推广,对α-闭子集遗传,被α-irresolute的广义Zadeh型函数所保持等.     

L-拓扑空间的相对β-紧性

在L-拓扑空间中引入相对β-紧性的概念,得到了它的一些性质,如它是L-好的推广,对β-闭子集遗传,被Mβ-连续的广义Zadeh型函数所保持等.     

p-仿紧空间

本文研究了p-仿紧空间和p-可数仿紧空间的相关问题.利用预开集和覆盖性质理论,得到了p-仿紧空间和p-可数仿紧空间的定义、等价刻画及αp-仿紧子集的性质,推广了一般拓扑学中仿紧空间的部分结果.     

谱表示

<正> Stone M.对Hilbert空间中一个具有简单谱的自伴算子建立了谱表示定理,即有实轴上的有限Borel测度μ,使得同构于L~2(μ),同时变A为乘以自变量λ的算子.Jauch等([2])讨论了一列交换的自伴算子完全集谱表示定理,但要求一个关于测度绝对连续性的假定.此外,依据约化理论([3])可知,如果A是可分Hilbert空间的自伴     

JOINT SPECTRAL SETS

Abstract

We consider the problem: if S,TEB(H) are commuting operators with von Neumann spectral sets X and Y respectively, does it imply that X x Y is a joint spectral set for the pair (S,T)?     

REPRESENTATION OF THE SPECTRAL SHIFT FUNCTION AND SPECTRAL ASYMPTOTICS FOR TRAPPING PERTURBATIONS

We obtain in the semi-classical setup of “black-box” long-range perturbations a representation for the derivative of spectral shift function ξ(λ) related to two self-adjoint operators L _j (h), j = 1,2. We show that the derivative ξ′(λ) is estimated by the norms of the cut-off resolvents of the operators L _j (h). Finally, we establish a Weyl type formula for the spectral shift function ξ(λ) generalizing the results of Robert [19] Robert, D. 1994. Relative time-delay for perturbations of elliptic operators and semiclassical asymptotics. J. Funct. Anal., 126: 36–82. [Crossref], [Web of Science ®] , [Google Scholar] and Christiansen [5] Christiansen, T. 1998. Spectral asymptotics for general compactly supported perturbations of the Laplacian on Rⁿ. Comm. P.D.E., 23: 933–947. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar].     

ON COMPLETELY SPECTRAL OPERATORS

In this paper we first introduce the concept of completely spectral operators and discuss its various properties; next, we consider spectral synthesis for this kind of operators and partly generalize Wermer’s result [1] on spectral synthesis for completely normal operators; finally, we investigate the problem of unitary equivalence of resolutions of the identity for completely spectral operators. Let \[\mathcal{X}\] be a separable Hilbert space and \[\mathcal{B}(\mathcal{X})\] the algebra of all bounded linear operators on \[\mathcal{X}\]. Let Lat T denote the lattice of all invariant subspaces of \[T \in \mathcal{B}(\mathcal{X})\] Definition 1. An operator \[T \in \mathcal{B}(\mathcal{X})\] is completely spectral if T is spectral and reductive. Proposition 1. T is a completely spectral operator if and only if T* is a completely spectral operator. Proposition 2. If T is a completely spectral operator and \[\mathcal{U} \in \] Lat T, then the restriction of T to \[\mathcal{U}\] is a completely spectral operator. Proposition 3. Let T be a spectral operator. If any pair of complementary subspaces of T is invariant under T, then T is similar to a completely spectral operator. Proposition 4. If T is a completely spectral operator, then T = N+Q, where N is a normal operator and Q is a quasinilpotent operator commuting with N. Moreover, every \[\mathcal{U} \in \] LatT reduces both N and Q. Difinition 2. We say that spectral synthesis holds for T, provided that for any \[\mathcal{U} \in \]LatT, which is not {0}, the set of root vectors of T contained in \[\mathcal{U}\] is complete in \[\mathcal{U}\]. Theorem 1, Let T be a completely spectral operator and let the set pf. root vectors of T be complete in \[\mathcal{U}\]. Then the spectral synthesis holds for T. The following lemma generalizes Theorem 5 of Dunford's [2]. Lemma. Let\[{E_{\text{1}}}(\sigma ),{E_2}(\sigma )\] be resolutions of the identity for bounded spectral operators T1, T2 respectively, on Banach space \[\mathcal{U}\], and let A be a bounded linear operator on \[\mathcal{U}\],If AT1 = T2A, then \[A{E_{\text{1}}}(\sigma ) = {E_2}(\sigma )A\]. Theoerm 2. Let T1, T2 be completely spectral operators. Their resolutions of the identity are \[{E_{\text{1}}}(\sigma ),{E_2}(\sigma )\], respectively. If T1 is a quasi-affine transform of T2, then ,\[{E_{\text{1}}}(\sigma )\] and \[{E_2}(\sigma )\] are unitarily equivalent.     

SPECTRAL AND SPECTRAL ELEMENT METHODS FOR HIGH ORDER PROBLEMS WITH MIXED BOUNDARY CONDITIONS

In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.     

人口算子的谱性质

本文讨论人口算子的谱性质,得到了人口算子本征值除可能有限个外均是代数单的,人口算子本征值新的分布性质,人口算子广义本征函数不构成基序列,Ｌ２［０,ｒ２］上的人口算子根子空间完整等．     

Sasakian子流形的谱几何

本文讨论了 Ｓａｓａｋｉａｎ子流形的谱几何,获得了复 Ｑｕａｄｒｉｃ上圆周丛以及全测地子流形的谱特征．     

BILINEAR SPECTRAL MULTIPLIERS ON HEISENBERG GROUPS

As we know,thus far,there has appeared no definition of bilinear spectral mul-tipliers on Heisenberg groups.In this article,we present one reasonable definition...     

Cahn—Hilliard方程的Legendre谱逼近

1.引 言本文我们将考虑非线性Cahn—Hilliard方程的初边值问题     

NEW SPECTRAL CHARACTERIZATIONS OF EXTREMAL HYPERSURFACES

Let M be a closed extremal hypersurface in Sn+1 with the same mean curva-ture of the Willmore torus Wm,n?m. We proved that if Specp(M)=Specp(Wm,n?m) for p=0, 1, 2, then M is Wm,m.