lp上单胞移位的拟幂零性(Ⅰ)

Let T denote a (unilateral, bilateral) weighted shift operator on any l^p for 1 < p<∞. in this paper we show that if T is unicellular, T is quasinilpotent . This answers a question of A. L. Shields.     

Ap(φ)上Toeplitz算子的半换位子

本文给出加权Bergman空间A^p(φ)上具有界调和符号的Toeplitz算子的半换位子为零或为紧算子的一些充要条件.     

椭圆型拟微分算子在LNP(Rn)中的Fredholm理论的Banach代数方法

本文利用Banach代数方法证明了伪微分算子N阶阵在L_N^p(Rⁿ)(p>1)中为Fredholm的充要条件是:相应的符号矩阵的行列式处处不为零.对p=2或N=1的特殊情况,此结果是人们所熟知的.     

Z/p2Z上幂零指数为3且平方同构于Np⊕Np的2秩代数

本文把这种代数的同构分类问题归结为素域F_p=Z/pZ上2阶一般线性群GL(2,F_p)作用于M_4,2(F_p)的2秩阵子集M_p上的轨道条数r(p)的求法问题,并以p=2,3为例具体给出r(2)=42,r(3)=149.     

Ap和Hp空间的乘子

给出了关于Ａ^p和Ｈ^p空间系数乘子的一些结果     

函数空间以及一类奇异积分算子在Hr(Rn)(p＜r≤1)中有界性的准则

在经典H^p(Rⁿ)空间原子分解理论基础上,给出了一种H^p(Rⁿ)空间的新的更为精细的刻划,籍此,给出了一类异奇积分算子在所有H^r(Rⁿ)(p＜r≤1)中有界性的准则     

一般环之因子幂零理想

本文称环Ω的左(右)理想A为因子幂零的,如果对于任意元素r∈Ω,均有正整数m=m(r),使得A^mr={0}.称Ω的一个左理想L为关于元素b∈Ω的左因子,如果Lb≠{0}.定理4 设R是环Ω的因子幂零右理想,那么R+ΩR是Ω的一个因子幂零理想.定理7 设Ω具有局部左因子极小条件,那么Ω的任意诣零左理想必是因子幂零左理想.本文指出因子幂零性是介于幂零性与诣零性之间的一种性质,更接近幂零性。     

关于Diophantine 方程xn+2kyn=pz2

设p 为奇素数且对任意的整数m, d, p≠(2^m±1)=/d², 则对任意的素数n > p^8p2, 方程xⁿ+2^kyⁿ=pz², k≥2 没有整数解(x, y, z) 使得x, y, z 两两互素且均不为0.     

SL(2,R)上一类极大算子的(H∞,s1,L1)型

本文我们引入了函数类B_δ(G//K)={φ∈L¹(G//K)||φ(t)|≤Δ^-1(t)(1+t)^1-δ,δ>0),对f∈L^p(G//K),1≤p≤∞,和极大算子(?),证明了这类算子是(H_∞,s¹,L¹)型的.     

关于环Fpm+uFpm+u2Fpm上循环码的注记

本文研究了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码分类.通过建立环F_p^m+uF_p^m+u²F_p^m到环F_p^m+uF_p^m的同态,给出了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码的新分类方法.应用这种方法,得到了环F_p^m+uF_p^m+u²F_p^m长度为p^s的循环码的码词数.     

LP (Rn) boundedness for the Marcinkiewicz integral

L^p (Rⁿ) boundedness is considered for the higher-dimensional Marcinkiewicz integral which was introduced by Stein. Some conditions implying the L^p(Rⁿ) boundedness for the Marcinkiewicz integral are obtained.     

Wr,p(R)-splines

In [3] Golomb describes, for 1 < p < ∞, the H^r,p(R)-extremal extension $\text{F}{}_1$ of a function $\text{?:E → R}$ (i.e., the H^r,p-spline with knots in E) and studies the cone $\text{H}{}_{1E}{}^{\mathrm{r,p}}$ of all such splines. We study the problem of determining when $\text{F}{}_1$ is in W^r,p ≡ H^r,p ∩ L^p. If $\text{F}{}_1\text{? W}{}^{\mathrm{r,p}}$, then $\text{F}{}_1$ is called a W^r,p-spline, and we denote by $\text{W}{}_{1E}{}^{\mathrm{r,p}}$ the cone of all such splines. If E is quasiuniform, then $\text{F}{}_1\text{? W}{}^{\mathrm{r,p}}$ if and only if . The cone $\text{W}{}_{1E}{}^{\mathrm{r,p}}$ with E quasiuniform is shown to be homeomorphic to l^p. Similarly, $\text{H}{}_{1E}{}^{\mathrm{r,p}}$ is homeomorphic to h^r,p. Approximation properties of the W^r,p-splines are studied and error bounds in terms of the mesh size $\text{¦ E ¦}$ are calculated. Restricting ourselves to the case p = 2 and to quasiuniform partitions E, the second integral relation is proved and better error bounds in terms of $\text{¦ E ¦}$ are derived.     

Subgroups of LF(2, 2n)

J. Gierster [Math. Ann. 26, 309–368] has proven a number of theorems giving the subgroup structure of LF(2, pⁿ), p an odd prime, and has given simple necessary and sufficient conditions for two elements of LF(2, pⁿ) to be conjugate. In this paper we obtain analogous theorems and conditions for LF(2, 2ⁿ). The methods involve solving congruences mod 2ⁿ.     

A note on cyclic codes over GR(p2, m) of length pk

The number of self-dual cyclic codes of length p ^k over GR(p ², m) is determined by the nullity of a certain matrix M(p ^k , i ₁). With the aid of Genocchi numbers, we determine the nullity of M(p ^k , i ₁) and hence determine completely the number of such codes.     

Lp (?m × ?n) boundedness for the Marcinkiewicz integral on product spaces

L^p(R^m × Rⁿ) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the L^p(R^m × Rⁿ) boundedness of the multiple Marcinkiewicz integral for some fixed 1 > p > ∞ are obtained.     

Topological singularities in W S,P ( S N , S 1)

We are interested in the location of the singularities of maps u ∈ W ^s,p (S ^N , S ¹) when 1 ≤ sp and 1 < sp < 2. To this end, we consider the distributional Jacobian. We show that the range of this operator on W ^s,p (S ^N , S ¹) is the closure in W ^s−2,p ⋂ W ^−1,sp of the set of N − 2-currents defined as the integration on smooth oriented N − 2-dimensional boundaryless submanifolds.     

On Extension of Isometries Between the Unit Spheres of Normed Space E and lP（p 〉 1）

In this paper, we study the extension of isometries between the unit spheres of normed space E and lP（p 〉 1）. We arrive at a conclusion that any surjective isometry between the unit sphere of normed space lP（p 〉 1） and E can be extended to be a linear isometry on the whole space lP（p 〉 1） under some condition.     

Quasi-permutation Representations of the Groups SU (3, q2) and PSU (3, q2)

A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful permutation representation of G is denoted by p(G). The minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers are denoted by q(G) and c(G) respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper p(G), q(G), c(G) and r(G) are calculated for the groups PSU (3, q²) and SU (3, q²).AMS Subject Classification (2000): 20C15     

Fast algorithms for determining the linear complexities of sequences over GF(pm) with the period 3n

In this paper, for the the primes p such that 3 is a divisor of p − 1, we prove a result which reduces the computation of the linear complexity of a sequence over GF(p ^m) (any positive integer m) with the period 3n (n and p ^m − 1 are coprime) to the computation of the linear complexities of three sequences with the period n. Combined with some known algorithms such as generalized Games-Chan algorithm, Berlekamp-Massey algorithm and Xiao-Wei-Lam-Imamura algorithm, we can determine the linear complexity of any sequence over GF(p ^m) with the period 3n (n and p ^m − 1 are coprime) more efficiently.     

A characterization of P2(μ) ≠ L2(μ)

It is shown that P²(μ) ≠ L²(μ) if and only if there exists a probability measure ν with ν ⊥ μ and 6pz.dfnc;_1,ν ? Cz.dfnc;pz.dfnc;_2,μ for all polynomials p and a fixed constant C < ∞. The relationship between this method and theorems of Berger and of Carey and Pincus concerning rationally cyclic vectors for powers of nonnormal subnormal Operators is examined.