符号空间有限型子转移混沌集的Hausdorff测度与Parry测度

设A是一个每列至少有二个元素为1的不可约0，1方阵，(∑4，σA)为由A所决定的符号空间有限型子转移．在∑A上定义一个与其拓扑相容的度量d使得(∑A，d)的Hausdorff维数为1．若G是H^-可测的σA的Li—Yorke混沌集，则H^1(C)＝0；若A是本原的，则存在一个σA的有限型混沌集S使得H^1(S)＝1，其中H^1为1-维的Hausdorff测度．  

符号空间及逆极限空间上的正混沌

本文推广Ｌｉ－Ｙｏｒｋｅ混沌定义，给出正混沌的定义，得到一类描述正混沌的符号动力 系统．并证明紧致度量空间上的连续映射正混沌的充要条件是其逆极限空间上的移位映射是 正混沌的．  

The Hausdorff Measure Theoretic Entropy of a Subshift in Symbolic Space

Ｉｎ [1 ]ａｎｄ [2 ]Ｘｉｏｎｇｉｎｔｒｏｄｕｃｅｄａｆｒａｃｔａｌｔｈｅｏｒｙｉｎｔｏｄｙｎａｍｉｃａｌｓｙｓｔｅｍｒｅｓｅａｒｃｈ ,ｍｅａｓｕｒｅｄｃｈａｏｔｉｃｓｅｔｓｗｉｔｈｔｈｅＨａｕｓｄｏｒｆｆｄｉｍｅｎｓｉｏｎａｎｄｔｈｅＨａｕｓｄｏｒｆｆｍｅａｓｕｒｅ .ＺｈｏｕｅｓｔｉｍａｔｅｄｔｈｅＨａｕｓｄｏｒｆｆｍｅａｓｕｒｅｏｆｆｉｎｉｔｅｔｙｐｅｓｕｂｓｅｔｉｎ [3].Ｉｎｔｈｉｓｐａｐｅｒ ,ｔｈｅＨａｕｓｄｏｒｆｆｍｅａｓｕｒｅｔｈｅｏｒｅｔｉｃｅｎｔｒｏｐｙｏｆａｓｕｂｓｈｉｆｔｉｎｓ…  

Dimensions of modified Besicovitch-Eggleston sets

We consider the variants of Besicovitch-Eggleston sets in symbolic spaces, and determine their fractal dimensions.  

NEW WAVELET BASES FOR NON-HOMOGENEOUS SYMBOLIC SPACE OpSm1,1 AND RELATED KERNEL-DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.  

有限型子集的Hausdorff测度

给出了有限型子集的Hausdorff测度的一个估计，改进了已有的结果。  

Chaos for Subshifts of Finite Type

This paper deals with chaos for subshifts of finite type. We show that for any subshift of finite type determined by an irreducible and aperiodic matrix, there is a finitely chaotic set with full Hausdorff dimension. Moreover, for any subshift of finite type determined by a matrix, we point out that the cases including positive topological entropy, distributional chaos, chaos and Devaney chaos are mutually equivalent.  

Hausdorff measure of sets of finite type of one-sided symbolic space

Some estimation formulae and a computation formula for the Hausdorff measure of the sets of finite type of the one-sided symbolic space are given. Project partially supported by the Natural Science Foundation of Guangdong Province and the Foundation of Advanced Research of Zhongshan University.  

EXTENSIONS OF HILBERT MODULES AND HANKEL OPERATORS

1.IntroductionInthepresentpaper,wewillcontinuethestudyofHilbertmodules[1-5].LetHbeaHilbertspaceandAafunctionalgebra.WesaythatHisaHilbertmoduleoverAifthereisamultiplication(a,f)-affromAxHtoH,makingHintoanXmoduleandif,inaddition,theactionisjointlycontinuousinthesup-normonAandtheHilbertspacenormonH.ThecategoryHofallHilbertNmodulesisanaturalsettingfornumerousquestionsinoperatortheory.In[9],DouglasandPaulseninitiatedasystematicstudyofHilbertmodules'theywereabletotranslatemanyconceptsandpro…  

NEW WAVELET BASES FOR NON－HOMOGENEOUS SYMBOLIC SPACE OpS1,1^m AND RELATED KERNEL－DISTRIBUTION SPACES

This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.