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.     

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.     

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.     

THE EXISTENCE OF RADIAL LIMITS OF ANALYTIC FUNCTIONS IN BANACH SPACES

Let X be a comPlex Banach space and let D be the open unit disc in the complex plane.We shall denote by H"(D, X) the Banach space consisting of all uniformly bounded X-vaued analytic functions defined on D equipped with the norm llflloo = suP lIf(z)Il. Az eDcomplex Banach space X is said to have the analytic Radon-NikOdym property if eachelemellt f E Hoo(D,X) has radial limits almost everywhere on the torus T = {e": 0 E[0, 2x]} (see [1]), this means that for almost all 0 C [0,27l, 9W…     

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.     

On Completeness and Minimality of Random Exponential System in a Weighted Banach Space of Functions Continuous on the Real Line

In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin's classical results.     

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.     

单位圆盘内代数体函数的唯一性定理

In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.     

Incompleteness of Complex Exponential System in L_α~p Space

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.     

Banach空间中有限族渐进伪压缩映象的迭代程序

Let E be a real Banach space and K be a nonempty closed convex and bounded subset of E. Let Ti ： K→ K, i=1, 2,... ,N, be N uniformly L-Lipschitzian, uniformly asymptotically regular with sequences {ε^（i）n} and asymptotically pseudocontractive mappings with sequences {κ^（i）n}, where {κ^（i）n} and {ε^（i）n}, i = 1, 2,... ,N, satisfy certain mild conditions. Let a sequence {xn} be generated from x1 ∈ K by zn：= （1-μn）xn＋μnT^nnxn, xn＋1 ：= λnθnx1＋ [1 - λn（1 ＋ θn）]xn ＋ λnT^nnzn for all integer n ≥ 1, where Tn = Tn（mod N）, and {λn}, {θn} and {μn} are three real sequences in [0, 1] satisfying appropriate conditions. Then ｜｜xn- Tixn｜｜→ 0 as n→∞ for each l ∈ {1, 2,..., N}. The results presented in this paper generalize and improve the corresponding results of Chidume and Zegeye, Reinermann, Rhoades and Schu.     

Approximate Controllability of Nonlinear Delay Integro Differential Evolution Equations with Random Impulses

The basic concept of this research is to analyse the approximate controllability (AC) of a nonlinear delay integrodifferential evolution system (NDIDES) with random impulse of the type \begin{align*}&z''(\zeta)=\mathfrak{A}(\zeta)z(\zeta)+(\mathfrak{B}x)(\zeta)+\int_{0}^{\zeta}\mathcal{H}(\zeta, s,z(\beta(s))), \ \sigma_{q} <\zeta < \sigma_{q+1}, \ \zeta\in [\zeta_{0}, \mathcal{T}], \\ &z(\sigma_{q})=a_{q}(\tau_{q})z(\sigma^{-}_{q}), ~~q = 1,2,\ldots,\\ &z_{\zeta_{0}}=\upsilon,\end{align*} by assuming that the linear system is approximately controllable. The existence and uniqueness of the mild solution to above system have been determined by using the Banach contraction principle and trajectory accessible sets. We generalize the results for NDIDES with and without fixed-type impulsive moments.     

On Algebraic Limits and Topological Properties of Sets of Möbius groups in $ \bar {R}^n $

Let G be the algebraic limit of a sequence $ \{ G_m\} $ of r generator subgroups of $ M(\bar {R}^n) $ . We prove that (i) if $ G_m $ is elementary, then G is elementary; (ii) if $ G_m $ is not non-elementary and non-discrete and G satisfies the Condition A, then G is not non-elementary and non-discrete. Let $ E_l = \{ (f_1, f_2,\ldots ,f_l): f_1,f_2,\ldots ,f_l\in M(\bar {R}^2), \langle \,f_1,f_2,\ldots , \,f_l \rangle\ elementary\} $ and $ D_l = \{ (f_1,f_2,\ldots ,f_l): f_1,f_2,\ldots ,f_l\in M(\bar {R}^2), \langle \,f_1,f_2,\ldots ,f_l \rangle\ discrete\} $ . we obtain that the set $ E_l , D_l\cup E_l $ and $ D_l\cap E_l^c $ are closed in $ \underbrace {M(\bar {R}^2)\times \cdots \times M(\bar {R}^2)}\limits _{l} $ .     

Hardy-Sobolev类上的Bohr型不等式

Let β 〉 0 and Sβ ：= {z ∈ C ： ｜Imz｜ 〈β} be a strip in the complex plane. For an integer r ≥ 0, let H∞^Г,β denote those real-valued functions f on R, which are analytic in Sβ and satisfy the restriction ｜f^（r）（z）｜ ≤ 1, z ∈ Sβ. For σ 〉 0, denote by Bσ the class of functions f which have spectra in （-2πσ, 2πσ）. And let Bσ^⊥ be the class of functions f which have no spectrum in （-2πσ, 2πσ）. We prove an inequality of Bohr type
‖f‖∞≤π/√λ∧σ^r∑k=0^∞（-1）^k（r＋1）/（2k＋1）^rsinh（（2k＋1）2σβ）,f∈H∞^r,β∩B1/σ,
where λ∈（0,1）,∧and ∧′are the complete elliptic integrals of the first kind for the moduli λ and λ′=√1- λ^2,respectively,and λ satisfies
4∧β/π∧′=1/σ.
The constant in the above inequality is exact.     

Structured backward error for palindromic polynomial eigenvalue problems

A detailed structured backward error analysis for four kinds of palindromic polynomial eigenvalue problems (PPEP)

Existence of Generalized Cauchy-Riemann Side-Systems in Several Complex Variables

In the present paper we have deduced the necessary and sufficient conditions on which an initial value problem $\fraca {\partial w}{\partial z_j} = a_j(z,\overline {z})\overline {w}+b_j(z,\overline {z})w+c_j(z,\overline {z}), \, j = 1,\ldots , n,\, w(z_0,\overline {z_0}) = w_0$ is locally solvable in the class of generalized analytic functions of several complex variables, which are functions fulfilling generalized Cauchy-Riemann System, $\fraca {\partial w}{\partial \overline {z_k}} = \overline {\alpha _k(z,\overline {z})}\, \overline {w}+ \overline {\beta _k(z,\overline {z})}w+ \overline {\gamma _k(z,\overline {z})},\, k = 1,\ldots , n$ .     

关于伪压缩映象不动点迭代的一点注记

设$K$是自反的并且具有一致Gateaux可微范数的Banach空间$E$的非空有界闭凸子集.设$T:K\rightarrow K$是一致连续的伪压缩映象.假设$K$的每一非空有界闭凸子集对非扩张映象具有不动点性质.设$\{\lambda_n\}$是$(0,\frac{1}{2}]$中序列满足: (i) $\lim_{n\rightarrow \infty}\lambda_n=0$; (ii) $\sum_{n=0}^{\infty}\lambda_n=\infty$.任给$x_1\in K$,定义迭代序列$\{x_n\}$为:$x_{n+1}=(1-\lambda_n)x_n+\lambda_nTx_n-\lambda_n(x_n-x_1),n\geq 1.$若$\lim_{n\rightarrow \infty}\|x_n-Tx_n\|=0$, 则上述迭代产生的$\{x_n\}$强收敛到$T$的不动点.     

角域内代数体函数的唯一性定理

Let W (z) and M(z) be v-valued and k-valued algebroidal functions respectively,(θ) be a b-cluster line of order ∞ (or ρ(r)) of W (z) (or M(z)).It is shown that W (z) ≡ M(z) provided E(a j ,W (z)) = E(a j ,M(z)) (j = 1,...,2v + 2k + 1) holds in the angular domain Ω(θ- δ,θ + δ),where b,a j (j = 1,...,2v + 2k + 1) are complex constants.The same results are obtained for the case that (θ) is a Borel direction of order ∞ (or ρ(r)) of W (z) (or M(z)).     

在${\mathbb{R}}^m$中重对数广义律的精确速率

令\{$X$, $X_n$, $n\ge 1$\}是期望为${\mathbb{E}}X=(0,\ldots,0)_{m\times 1}$和协方差阵为${\rm Cov}(X,X)=\sigma^2I_m$的独立同分布的随机向量列, 记$S_n=\sum_{i=1}^{n}X_i$, $n\ge 1$. 对任意$d>0$和$a_n=o((\log\log n)^{-d})$, 本文研究了${{\mathbb{P}}(|S_n|\ge (\varepsilon+a_n)\sigma \sqrt{n}(\log\log n)^d)$的一类加权无穷级数的重对数广义律的精确速率.