预解算子族的一个推广

本文引入了正则预解族的概念,给出了其若干性质及两个特征,所得结果推广了预解算子族的相应结果．     

双连续C正则预解算子族的生成定理

基于C正则预解算子族和双连续C_0半群引入了双连续C正则预解算子族的概念,考察了双连续C正则预解算子族生成元与预解式之间的关系,给出了双连续C正则预解算子族Hille-Yosida型生成定理,从而对Bananch空间强连续半群的生成定理进行了推广.     

拟微分算子与正则余弦函数

设Ｏｐｐ（ｆ）是Ｌｐ（Ｒｎ）（１ｐ＜∞）中具有象征ｆ∈Ｓｍρ，０的常系数拟微分算子．本文证明了在适当条件下，Ｏｐｐ（ｆ）在Ｌｐ（Ｒｎ）（１ｐ＜∞）中生成一个正则余弦函数，并将所得结果应用到对应的非齐次二阶Ｃａｕｃｈｙ问题．     

多元Stancu算子的Boolean和迭代

定义单纯形上高维Stancu算子的Boolean和迭代算子并且研究它逼近连续函数的正定理、逆定理与饱和定理，得到了较高的逼近阶．     

正则预解算子族的乘积扰动

设K∈C（R＋）和B是一个有界线性算子．作者证明如果犃生成一个指数有界的A正则预解算子族，那么BA，AB或A（I＋B），（I＋B）A也生成一个指数有界的k-正则预解算子族．此外，作者也给出了k正则预解算子族的加法扰动的相应结果．     

Several Formulas for the First Regularized Trace of Discrete Operators

We derive several abstract formulas (of Gelfand--Levitan type) for the first regularized trace of discrete operators under various conditions convenient for verification. The proof of the main result is based on the contour integration method with some modifications from analytic perturbation theory and from the approach proposed earlier by M. Dostani. Some known trace formulas are generalized and improved. We give examples of the applications of our abstract trace formulas for obtaining special trace formulas for ordinary differential operators and for partial differential operators.     

Maximum Norm Resolvent Estimates for Elliptic Finite Element Operators

We study a finite element approximation A _h, based on simplicial Lagrange elements, of a second order elliptic operator A under homogeneous Dirichlet boundary conditions in two and three dimensions, where h is thought of as a meshsize. The main result of the paper is a new resolvent estimate for the operator A _h in the L -norm. This estimate is uniform with respect to h for the case with at least quadratic elements. In the case with linear elements, the estimate contains on the right a factor proportional to (log log ), where = 1 or = in two or three dimensions, respectively.This revised version was published online in October 2005 with corrections to the Cover Date.     

Exponential Sums and Coding Theory: A Review

This article is a survey of several recent applications of methods from analytic number theory to research in coding theory, including results on Kloosterman codes, binary Goppa codes, and prime phase shift sequences. The mathematical methods focus on exponential sums, in particular Kloosterman sums. The interrelationships with the Weil–Carlitz–Uchiyama bound, results on Hecke operators, theorems of Bombieri and Deligne and the Eichler–Selberg trace formula are reviewed.     

Commuting Toeplitz Operators on the Pluriharmonic Bergman Space

We prove that two Toeplitz operators acting on the pluriharmonic Bergman space with radial symbol and pluriharmonic symbol respectively commute only in an obvious case.     

Resolvent Estimates for Fleming–Viot Operators with Brownian Drift

This article is a supplement to the paper of D. A. Dawson and P. March (J. Funct. Anal.132(1995), 417–472). We define a two-parameter scale of Banach spaces of functions defined on ₁( ^d), the space of probability measures ond-dimensional euclidean space, using weighted sums of the classical Sobolev norms. We prove that the resolvent of the Fleming–Viot operator with constant diffusion coefficient and Brownian drift acts boundedly between certain members of the scale. These estimates gauge the degree of smoothing performed by the resolvent and separate the contribution due to the diffusion coefficient and that due to the drift coefficient.     

Commuting Differential and Difference Operators Associated to Complex Curves I

The purpose of this paper is to define functional realizations of the Khizhnik–Zamolochikov–Bernard (KZB) connection on the bundle of conformal blocks over the moduli space of curves.     

Commuting Rank 2 Differential Operators Corresponding to a Curve of Genus 2

We construct commuting rank 2 formally self-adjoint ordinary differential operators corresponding to a curve of genus 2.     

Commuting Dual Toeplitz Operators on the Polydisk

On the polydisk, the commutativity of dual Toeplitz operators is studied. We obtain characterizations of commuting dual Toeplitz operators, essentially commuting dual Toeplitz operators and essentially semi-commuting dual Toeplitz operators.     

多圆盘Bergman空间上Toeplitz算子的乘积和交换性

该文给出了多圆盘Bergman空间上两个带有某种符号的Toeplitz算子的乘积等于另一个Toeplitz算子的充分必要条件,并且给出了乘积算子所带符号的公式.接下来,相应的研究了它的交换性.这些研究结果都是根据符号函数的Mellin变换.     

Wave Front Set at Infinity and Hyperbolic Linear Operators with Multiple Characteristics

We discuss a notion of wave front set which allows us tocontrol the behaviour `at infinity' of temperate distributions. Weobtain the microlocality and microellipticity properties with respect toa class of global pseudodifferential operators and a propagation theoremfor the corresponding class of Fourier Integral Operators. Through theseresults, we prove an adapted global version of the classical theoremconcerning the singularities of solutions of hyperbolic Cauchy problemsfor linear operators with multiple characteristics of constantmultiplicities. Finally, we make a comparison with the scattering wavefront set introduced by Melrose.