复指数函数系的极小性

A sufficient condition is obtained for the minimality of the complex exponential system E（A, M） = {z^le^λnz： l = 0, 1,,.., mn - 1; n = 1, 2,...} in the Banaeh space La^p consisting of all functions f such that f^-a ∈ LP（N）. Moreover, if the incompleteness holds, each function in the closure of the linear span of exponential system E（A, M） can be extended to an analytic function represented by a Taylor-Dirichlet series.     

复指数系统在$L_{\alpha}^{p}$空间的不完备性

A necessary and sufficient condition is obtained for the incompleteness of complex exponential system in the weighted Banach space Lαp = {f：∫＋∞∞ ｜f（t）e-α（t）｜pdt ＋∞},where 1 ≤ p ＋∞ and α（t） is a weight on R.     

上密度无限制的指数多项式逼近

We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined on the real axis R satisfying ＋∞ ∞ ｜f（t）｜ p e -α（t） dt） 1/p ,1 p ∞,and α（t） is a nonnegative continuous function defined on the real axis R.In this paper,the upper density of the sequence which forms the exponential polynomials is not required to be finite.In the study of weighted polynomial approximation,consideration of the case is new.     

有限uM,D-正交指数函数系的一个充分条件

设$\mu_{M,D}$是由仿射迭代函数系$\{\phi_{d}(x)=M^{-1}(x+d)\}_{d\in D}$唯一确定的自仿测度, 它的谱与非谱性质与Hilbert空间$L^{2}(\mu_{M,D})$中正交指数函数系的有限性和无限性有着直接的关系. 本文将利用矩阵的初等变换给出$\mu_{M,D}$\,{-}\!\!正交指数函数系有限性的一个充分条件. 由于这个条件只与 矩阵$M$的行列式有关, 因此, 它在$\mu_{M,D}$的非谱性的判断方面便于直接验证.     

Banach空间中复指数函数系的不完备性

In this paper, we obtain a necessary and sufficient condition for the incompleteness of complex exponential system in Cα, where Cα is a weighted Banach space of complex continuous functions f on the real axis R with f(t) exp{-α(t)}vanishing at infinity, in the uniform norm.     

随机指数系的完备性和极小性

得到了随机指数系在加权Banach空间C_α中完备和极小的充要条件,其中C_α是实直线R上的复连续函数在权α的一致范数下组成的Banach空间.这些结果可以看作是Malliavin经典结果的概率推广.     

随机指数系的完备性和极小性

得到了随机指数系在加权Banach空间Cα中完备和极小的充要条件,其中Cα是实直线R上的复连续函数在权α的一致范数下组成的Banach空间.这些结果可以看作是Malliavin经典结果的概率推广.     

型空间中随机指数函数系的完备性

该文采用了新的方法来研究由整函数组成的满足 ( ∫∫_C| f(z)|^pe^-α(|z|)dm_z)^1/p <∞ (1 < p <∞) 的Fock型空间中随机指数函数系的完备性. 还对于实轴上的加权Banach 空间讨论了类似的问题     

Fock型空间中随机指数函数系的完备性

该文采用了新的方法来研究由整函数组成的满足的Fock型空间中随机指数函数系的完备性.还对于实轴上的加权Banach空间讨论了类似的问题.     

复指数函数系在Lpα空间中的完备性

A necessary and sufficient condition is obtained for the complex exponential system to be dense in the weighted Banach space Lpα = {f : f∞-∞ |f(t)e-α(t)|pdt ∞}, where 1 ≤ p + ∞and α(t) is a nonnegative continuous function on R.     

Incompleteness and minimality of complex exponential system

A necessary and sufficient condition is obtained for the incompleteness of a complex exponential system E(A,M)in C_α,where C_αis the weighted Banach space consisting of all complex continuous functions f on the real axis R with f(t)exp(-α(t))vanishing at infinity,in the uniform norm‖f‖_α=sup{|f(t)e~(-α(t))|:t∈R}with respect to the weightα(t).If the incompleteness holds, then the complex exponential system E(?)is minimal and each function in the closure of the linear span of complex exponential system E(?)can be extended to an entire function represented by a Taylor-Dirichlet series.     

加权Banach空间上的复指数系的闭包

In this paper,closure of the linear span on complex exponential system in weighted Banach space Lαp is studied.Each function in the closure of complex exponential system can be extended to an entire function represented by Taylor-Dirichlet series.     

Minimality and reductibility of conditionally poisson systems with finite state space

In this paper we consider stochastic systems with finite state space and counting process output. In particular we address the question whether a given system has a minimal representation, where roughly speaking minimality means minimality of the size of the state space. We show that minimality is connected to a suitably defined notion of observability. Finally we present an algorithm that enables us, starting from a given representation, to construct a minimal representation for the same system