约化代数的交换子及正常算子的n次根

本文证明了Hilbert空间上正常算子的n次根具有性质(p),也证明了,当f(T)为可对角线算子时,T具有性质(p),其中f(z)为σ(T)上的非平凡解析函数,这些结果是C.K.Fong等关于代数算子相应结果的推广。 本文最后证明了当T为θ类算子且为某个正常算子的n次根,那么T的自交换子[T~*,T]的零空间约化T,因而如果u∈Lat T并且T在u上限制为正常算子,那么u是T的约化子空间。     

*-A(n)算子的谱性质

主要给出了*-A(n)算子的一些性质:若T是*-A(n)算子,则T有谱的连续性;若T是*-A(n)算子,则T的近似点谱和联合近似点谱是相等的;若T,S是*-A(n)算子,则T,S是Weyl算子当且仅当TS是Wey1算子.     

关于非正常算子组的联合数值域

本文研究非正常算子组的联合数值域,主要结果如下: 1.设T=(T_1,…,T_n)是n元算子组,则∑(T)的端点全在内.从而,∑(T)=CoW(T).这里W(T)和∑(T)分别表示T的联合数值域和代数型联合数值域. 2.如果Ext∑(T)σ_π(T),那么是C~n的凸子集.特别地,如果T=(T_1,…,T_n)是交换算子组,则有W(T)=CoSp(T). 3.设T=(T_1,…,T_n)是具有交换正常扩张算子组的交换次正常算子组或重交换亚正常算子组.当λ∈ExtΣ(T)并且时,这里‖x_ν‖=1,则有(T_j—λ_j)x_ν→0 (ν→∞,1≤j≤n).从而W(T)是C~n的凸子集,并且W(T)=CoSp(T). 4.设T=(T_1,…,T_n)是重交换的亚正常算子组,T(α)=(T_1(α_1),…,T_n(α_n))(α∈[0,1]~n)是T的广义记号算子组.则     

拟-*-A(n)算子的谱性质

我们证明了以下结论:(1)若T是拟-*-A(n)算子,则T是似正规算子.(2)若E是拟-*-A(n)算子T的非零孤立谱点λ的Riesz幂等算子,则E是自共轭的且满足R(E)=N(T-λ)=N(T-λ)*.(3)若T或T^*是代数拟-*-A(n)算子,则f(T)满足Weyl定理.(4)若T*是代数拟-*-A(n)算子,则f(T)满足Weyl定理.(4)若T^*是代数拟-*-A(n)算子,则f(T)满足α-Weyl定理,其中f∈H(σ(T)).     

关于广义Aluthge变换的谱性质的研究

设T∈H（H），T=U｜T｜是算子T的极分解，则定义T^λ=｜T｜^λU｜T｜^1-λ和T^λ（＊）=｜T＊｜^λU｜T＊｜^1-λ，（其中0〈λ〈1）分别为算子的广义Aluthge变换和广义＊-Aluthge变换．本文中主要研究了三者之间的几种谱的关系．同时，还证明了算子T满足修正的Weyl定理当且仅当弘满足修正的Weyl定理当且仅当T^λ（＊）满足修正的Weyl定理．最后证明了算子T满足a—Weyl定理当且仅当T^λ满足a—Weyl定理．     

Dirichlet空间上一类积分算子的约化子空间

刻画了 n移位算子加带特定权的Volterra算子T1在Dirichlet空间上的相似性,利用算子理论技巧证明了T1在Dirichlet空间上的作用和乘法算子Mp在空间S(D)上的作用相似,进一步证明了当p(z)=zn时相应的算子T2有2n个约化子空间.     

有限BIR分解在相似下唯一的一类算子

本文证明了H~p(T)(1≤p≤∞)空间上以n阶Blaschke乘积为符号的Toeplitz算子相似于⊕_nT_z,从而证明了这类算子的有限BIR分解在相似下唯一．     

Clifford分析中具有超正则核的T算子的性质

讨论了Clifford分析中具有超正则核的T(Ieodorescu)算子的基本性质.T算子是定义在区域上的奇异积分算子,它在广义解析函数理论和Vekua理论中起着重要的作用.在复分析中关于T算子的理论已经发展得很完善,但在Clifford分析中,具有超正则核的T算子的相关性质还没有得到研究.研究了Clifford分析中具有超正则核的T算子的基本性质,得到了这个算子在ΩR_+~(n+1)上的一致有界性,Hlder连续性以及这个算子的γ次可积性.     

算子n次方根的惟一性

B(H)表示定义在希尔伯特空间H上的所有有界线性算子的全体。对于A∈B(H),其中σ(A)和W(A)分别表示算子A的谱和数值域,N表示自然数集。关于算子A的n(n∈N)次方根,本文的主要结果是:(1)若σ(A)∩(-∞,0]=φ,则A有惟一的n次方根B∈B(H)且σ(B)(?)~(2/n)~o;(2)若(?)∩(-∞,0]=φ,则A有惟一的n次方根B∈B(H)且(?)(2/n)~o这里,S_(1/n)={λ∈C‖argλ|≤(1/2n)π}且S_(1/n)~o表示集合S+(1/n)的内部。     

具有无限重数的算子到正规算子集的距离估计与不可分的BDF定理

设T为Hilbert空间H上的有界线性算子,T~((n))表示n个T的直和,其中n=1,2,...,∞.本文给出了T~((∞))到全体正规算子的距离估计,并指出T~((n))到正规算子集的距离会因n是否为∞而引起大幅的变化.借助于该距离估计,本文证明了,若H为不可分Hilbert空间,K为B(H)的非紧算子理想,则B(H)/K中的正规算子都可表示为B(H)中的一个正规算子与K中的一个算子之和.     

Error diffusion on simplices: The structure of bounded invariant tiles

This is a companion paper to Adleret al. (in press, 2015). There, we proved the existence of an absorbing invariant tile for the Error Diffusion dynamics on an acute simplex when the input is constant and “ergodic” and we discuss the geometry of this tile. Under the same assumptions we prove here that said invariant tile (a fundamental set of the lattice generated by the vertices of the simplex) which is a finite union of polytopes have the property that any union of the intersections of the tile with the Voronoï regions of the vertices is a tile for a different, explicitly defined lattice.     

Ribbon tile invariants

Let be a finite set of tiles, and a set of regions tileable by . We introduce a tile counting group as a group of all linear relations for the number of times each tile can occur in a tiling of a region . We compute the tile counting group for a large set of ribbon tiles, also known as rim hooks, in a context of representation theory of the symmetric group.

The tile counting group is presented by its set of generators, which consists of certain new tile invariants. In a special case these invariants generalize the Conway-Lagarias invariant for tromino tilings and a height invariant which is related to computation of characters of the symmetric group.

The heart of the proof is the known bijection between rim hook tableaux and certain standard skew Young tableaux. We also discuss signed tilings by the ribbon tiles and apply our results to the tileability problem.

     

企业债券的欧式期权的定价公式

本文研究了带有信用风险的企业债券的欧式衍生资产的定价方法,建立风险债券与无风险债券期权价格的相互关系。     

非对称广义自回归条件异方差的新模型

本文提出了一个新的非对称广义自回归条件异方差的新模型,证明了该模型宽平稳及其最简模型偶数价矩存在的充要条件。     

Aperiodic Tilings with One Prototile and Low Complexity Atlas Matching Rules

We give a constructive method that can decrease the number of prototiles needed to tile a space. We achieve this by exchanging edge-to-edge matching rules for a small atlas of permitted patches. This method is illustrated with Wang tiles, and we apply our method to present via these rules a single prototile that can only tile ℝ³ aperiodically, and a pair of square tiles that can only tile ℝ² aperiodically.     

Hexagon tilings of the plane that are not edge-to-edge

Acta Mathematica Hungarica - An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer...     

一类自相似tile成为框架集的充分必要条件

本文研究了数字集具有严格乘积形式的自相似tile成为框架集的问题.利用Zak变换,证明了自相似tile是框架集的充要条件是其数字集D={0,1,2…,N-1}.     

Combinatorially Regular Polyomino Tilings

Let T be a regular tiling of ℝ² which has the origin 0 as a vertex, and suppose that φ: ℝ² → ℝ² is a homeomorphism such that (i) φ(0)=0, (ii) the image under φ of each tile of T is a union of tiles of T, and (iii) the images under φ of any two tiles of T are equivalent by an orientation-preserving isometry which takes vertices to vertices. It is proved here that there is a subset Λ of the vertices of T such that Λ is a lattice and φ|_Λ is a group homomorphism. The tiling φ(T) is a tiling of ℝ by polyiamonds, polyominos, or polyhexes. These tilings occur often as expansion complexes of finite subdivision rules. The above theorem is instrumental in determining when the tiling φ(T) is conjugate to a self-similar tiling.     

A NEW PSEUDOSPECTRAL APPROXIMATION FOR THE FOWARD-BACKWARD HEAT EQUATION

ＡＮＥＷＰＳＥＵＤＯＳＰＥＣＴＲＡＬＡＰＰＲＯＸＩＭＡＴＩＯＮＦＯＲＴＨＥＦＯＷＡＲＤ－ＢＡＣＫＷＡＲＤＨＥＡＴＥＱＵＡＴＩＯＮ￥ＹｅＸｉｎｇｄｅ（叶兴德）ＪｉａｎｇＪｉｎｓｈｅｎｇ（江金生）（Ｄｅｐｔ．ｏｆＭａｔｈ．＆Ｉｎｆｏｒ．Ｓｃｉ．，Ｈａｎｇ...     

Some tilings of the plane whose singular points are uncountable and unbounded

Let I be a tiling of the plane such that for every tile T of I there correspond a tile T of I (not necessarily unique) and an integer k(T, T) (depending on T and T), k(T, T)>2, such that T meets T in k(T, T) connected components. Tiles T and T satisfying this condition are called associated tiles in I. Various properties concerning I and its singular points are obtained. First, it is not possible that every tile in I have a unique associated tile. In fact, there exist infinite families of tiles {F} {F _n:n1} such that F is the unique associated tile for every F _n. Next, if x is a singular point of I, then every neighborhood of x contains uncountably many singular points of I. Finally, the set of singular points of I is unbounded.