有限维弱空间的维数定理

向量空间的维数公式，可以推广到比子空间更广的一类弱空间。     

d维平稳高斯过程多重点的Hausdorff维数及Packing维数

设Ｘ＾ｄ（ｔ）（ｔ∈Ｒ＋）是ｄ维可分平稳高斯过程，在一定条件下，本文得到了Ｘ＾ｄ（ｔ）的ｋ重点集的Ｈａｕｓｄｏｒｆｆ维数及Ｐａｃｋｉｎｇ维数。Ｐｏｌｙａ过程为其特例。     

Hausdorff维数和Packing维数

设W~(t)∶R N→Rd是N指标d维广义W inner过程,Bore l集E1,…,Em RN>.本文研究了在一定条件下,m项代数和W~(E1)W~(E2)…W~(Em)的H ausdorff维数和Pack ing维数的有关结论,其结果推广了文[3]的相关结果。     

$A_n-$型有限维代数的整体维数

设$k$是一个代数闭域, $n$是一个自然数,本文给出了一个精确刻画$A_{n}$-型有限维$k$-代数的整体维数的技巧.据此给出了$A_{n}$-型有限维$k$-代数的所有可能的整体维数.特别的,如果$n>1$,我们指出其中最大的是 $n-1$,最小的是 $1$.     

d维平稳高斯过程极集的充分条件及维数

本文研究了d维平稳高斯过程极集的性质,给出了d维平稳高斯过程广义极性的充分条件,并通过一个特殊的Cantor型集的构造将极集的维数与容度巧妙地结合起来,得到了d维平稳高斯过程非极集的Hausdorff维数的下确界.     

螺线的Steinhaus维数

Ｄｕｐａｉｎ Ｙ,Ｆｒａｎｃｅ Ｍ．Ｍ．和 Ｔｒｉｃｏｔ Ｃ．［１］利用积分几何中的经典的Ｓｔｅｉｎｈａｕｓ定理,引入 Ｓｔｅｉｎｈａｕｓ维数,并研究了螺线的 Ｓｔｅｉｎｈａｕｓ维数与盒维数的关系．本文深入这一研究,对Ｓｔｅｉｎｈａｕｓ维数的值域,单调性等基本性质作了进一步的考察．     

R^d中Hausdorff维数和packing维数的确定

本文目的在于建立确定Ｒ＾ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ和ｐａｃｋｉｎｇ维数Ｄｉｍ的两个命题，进而寻求Ｒ＾ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ与ｐａｃｋｉｎｇ维数Ｄｉｍ相等的条件；这使得我们能够引入分形测度的测度论定义。     

一类递归集Hausdorff维数及Bouligand维数

本语言给出了递归集的Ｈａｕｓｄｏｒｆｆ维数的下界估计，并由此确定了一类递归集的维数，所获结果包含并推广了Ｂｅｄｆｏｒｄ，Ｄｅｋｋｉｎｇ及文志英，钟红柳等人的有关结果。     

d维平稳高斯过程多重时的Hausdorff维数及Packing维数

设X^d(t∈R )是d维可分平衡高,过程,在一定条件下,本文得到了x^d(t)多重时Hausdorff维数及Packing维数,Polya过程为其特例。     

一类二维非线性Schroedinger方程的吸引子及其维数

本研究了一类二维非线性Schrodinger方程解的有限维行为，我们得到了此方程存在吸引子，并得到了此吸引子维数的上界估计     

A Unified Approach to Optimal Feedback in the Infinite-Dimensional Linear-Quadratic Control Problem with an Inequality Constraint on the Trajectory or Terminal State

This paper develops a unified approach to optimal feedback controlin the infinite-dimensional linear-quadratic control problemwith an inequality constraint on the trajectory or terminalstate. A general abstract Hilbert-space framework for the problemis provided, and then the results are specified to concreteoptimal problems for a linear infinite-dimensional system whichallows unboundedness in the input and output operators. In allcases, the same technique is used in order to obtain the optimalcontrol in feedback form; in some cases, the differential Riccatiequation is derived for the optimal cost operator.     

Hypercyclic subspaces in Fréchet spaces

In this note, we show that every infinite-dimensional separable Fréchet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of bounded operators when endowed with the strong operator topology. This completes the earlier work of several authors.

     

On Semitransitive Collections of Operators

A collection F of operators on a vector space V is said to be semitransitive if for every pair of nonzero vectors x and y in V there exists a member T of F such that either Tx = y or Ty = x (or both). We study semitransitive algebras and semigroups of operators. One of the main results is that if the underlying field is algebraically closed, then every semitransitive algebra of operators on a space of dimension n contains a nilpotent element of index n. Among other results on semitransitive semigroups, we show that if the rank of nonzero members of such a semigroup acting on an n-dimensional space is a constant k, then k divides n.     

Existence and nonexistence of hypercyclic semigroups

In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinite-dimensional Banach space that is very different from--and considerably shorter than--the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite-dimensional Fréchet space. This complements recent results due to Bès and Chan. Moreover, we discuss the Hypercyclicity Criterion for semigroups and we give an example of a separable infinite-dimensional locally convex space which supports no supercyclic strongly continuous semigroup of operators.

     

Products of positive operators

A new, very simple proof is given of a result of P. Y. Wu which asserts that every unitary operator on an infinite-dimensional Hilbert space is a product of positive operators.

     

On the Finite-dimensional Optimal Approximations to the Infinite dimensional Linear Operators

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＨａｎｄＫｂｅｒｅａｌｏｒｃｏｍｐｌｅｘｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌＨｉｌｂｅｒｓｐａｃｅ．Ａ（ｂｏｕｎｄｅｄｌｉｎｅａｒ）ｏｐ－ｅｒａｔｏｒＡ：Ｈ→Ｋｉｓｓａｉｄｔｏｂｅｉｎｆｉｎｉｔｅ－ｄｉｍｅｎｓｉｏｎａｌ（ｏｒ,ｆｉｎｉｔｅ－ｄｉｍｅｎｓｉｏｎａｌ）ｉｆｔｈｅｒａｎｇｅｏｆＡｉｓｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌ（ｏｒ,ｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌ）．Ａｉｓｓａｉｄｔｏｂｅｎ－ｄｉｍｅｎｓｉｏｎａｌｉｆｔｈｅｒａｎｇｅｏｆＡｉｓｎ…     

Super-Ergodic operators

The aim of this work is to study operators naturally connected to Ergodic operators in infinite-dimensional Banach spaces, such as Uniform-Ergodic, Cesaro-bounded and Power-bounded operators, as well as stable and superstable operators. In particular, super-Ergodic operators are introduced and shown to be strictly between Ergodic and Uniform-Ergodic operators, and that any power bounded operator is super-Ergodic in a superreflexive space. New relationships between these operators are shown, others are proven to be optimal or can be ameliorated according to structural properties of the Banach space, such as the superreflexivity or with unconditional basis.

     

Weakly open sets in the unit ball of some Banach spaces and the centralizer

We show that every Banach space X whose centralizer is infinite-dimensional satisfies that every non-empty weakly open set in BY has diameter 2, where (N-fold symmetric projective tensor product of X, endowed with the symmetric projective norm), for every natural number N. We provide examples where the above conclusion holds that includes some spaces of operators and infinite-dimensional C^∗-algebras. We also prove that every non-empty weak^∗ open set in the unit ball of the space of N-homogeneous and integral polynomials on X has diameter two, for every natural number N, whenever the Cunningham algebra of X is infinite-dimensional. Here we consider the space of N-homogeneous integral polynomials as the dual of the space (N-fold symmetric injective tensor product of X, endowed with the symmetric injective norm). For instance, every infinite-dimensional L₁(μ) satisfies that its Cunningham algebra is infinite-dimensional. We obtain the same result for every non-reflexive L-embedded space, and so for every predual of an infinite-dimensional von Neumann algebra.     

二次算子族及非负无穷维Hamilton算子的谱分布

本文讨论了一类在弦和梁的微小振动中出现的二次算子族L(λ)=λ~2MλK-A的谱分布问题,进而将所得结论与无穷维Hamilton算子联系起来,利用无穷维Hamilton算子的特殊结构,得到了一类非负无穷维Hamilton算子的谱分布,这为无穷维Hamilton算子的半群方法提供了理论保证.     

Frequently hypercyclic subspaces

We study the existence of frequently hypercyclic subspaces for a given operator, that is, the existence of closed infinite-dimensional subspaces in which every non-zero vector is frequently hypercyclic. We attack the problem with any of the three methods that have been used for hypercyclic subspaces: a constructive approach, an approach via left-multiplication operators, and an approach via tensor products.