球上的局部多项式框架

正交展开诱导的次指数局部化核与框架

Sub-exponentially localized kernels and frames induced by orthogonal expansions

本文的目的是构造超指数局部化核和框架的背景下，经典的正交展开，即展开的雅可比多项式，球调和函数，正交多项式上的球和单纯形，Hermite和Laguerre函数。

Highly localized kernels on the sphere induced by Newtonian kernels

The purpose of this article is to construct highly localized summability kernels on the unit sphere in ${\mathbb R}^d$ that are restrictions to the sphere of linear combinations of a small number of shifts of the fundamental solution of the Laplace equation (Newtonian kernel) with poles outside the unit ball in ${\mathbb R}^d$. The same problem is also solved for the subspace ${\mathbb R}^{d-1}$ in ${\mathbb R}^d$.

球上加权Triebel-Lizorkin和Besov空间的分解

Decomposition of weighted Triebel-Lizorkin and Besov spaces on the ball

引入并研究了$\Rd$中单位球$B^d$上的加权Triebel-Lizorkin空间和Besov空间，它们的权为$\W(x)= (1-|x|^2)^{μ-1/2}$，$μ\ge 0$.一个分解方案的开发方面几乎指数本地化的多项式元素（针）$\{ϕ_ξ\}$，$\{ψ_ξ\}$和它示出的分布的成员资格的加权Triebel-Lizorkin或Besov空间可以确定的针系数$\{\ip{f,ϕ_ξ}\}$在适当的数列空间的大小。

Approximation and localized polynomial frame on conic domains

Highly localized kernels constructed by orthogonal polynomials have been fundamental in recent development of approximation and computational analysis on the unit sphere, unit ball and several other regular domains. In this work we first study homogeneous spaces that are assumed to contain highly localized kernels and establish a framework for approximation and localized tight frame in such spaces, which extends recent works on bounded regular domains. We then show that the framework is applicable to homogeneous spaces defined on bounded conic domains, which consists of conic surfaces and the …

单位球上向量值函数Bergman空间上算子的本质范数

The Essential Norm of Operators on the Bergman Space of Vector--Valued Functions on the Unit Ball

设$A_α^{p}(\mathbb{B}^n;\mathbb{C}^d)$是取值于$\mathbb{C}^d$的函数的$\mathbb{C}^n$的单位球$\mathbb{B}^n$上的加权Bergman空间。对于$1<p<\infty$，设$\mathcal{T}_{p,α}$是由具有有界矩阵值符号的Toeplitz算子的有限乘积的有限和生成的代数（在$d=1$的情况下称为Toeplitz代数）。我们证明了每一个$S\in \mathcal{T}_{p,α}$都可以用局部化算子来近似。这将用于获得$\mathcal{T}_{p,α}$中算子的本质范数的几个等价表达式。然后，我们用它来描述$A_α^{p}(\mathbb{B}^n;\mathbb{C}^d)$中的紧算子。主要结果推广了以前的结果，并指出算子在$A_α^{p}(\mathbb{B}^n;\mathbb{C}^d)$中是紧的当且仅当它在$\mathcal{T}_{p,α}$中且其Berezin变换在边界上为零.