Convolution operators via orthogonal polynomials

多元正交多项式。I

Orthogonal polynomials in several variables. I

本文引入并讨论了几类多元非交换正交多项式。重点是一个非交换版本的正交多项式的实数线。我们介绍这些多项式的递归方程，Christoffel-Darboux公式和Jacobi型矩阵。

多元正交多项式

Multi-variable orthogonal polynomials

刻画了有限原子数的$\mathbb{R}^d$上的原子概率测度.我们进一步证明了与多重Hermite（resp. Laguerre，resp. Jacobi）正交多项式是对角矩阵。最后，作为多Jacobi正交多项式情形的推广，给出了Gegenbauer，Chebyshev和Legendre正交多项式的Jacobi序列.

Self-inversive polynomial and quasi-orthogonality on the unit circle

In this paper we study quasi-orthogonality on the unit circle based on the structural and orthogonal properties of a class of self-invariant polynomials. We discuss a special case in which these polynomials are represented in terms of the reversed Szegő polynomials of consecutive degrees and illustrate the results using contiguous relations of hypergeometric functions. This work is motivated partly by the fact that recently cases have been made to establish para-orthogonal polynomials as the unit circle analogues of quasi-orthogonal polynomials on the real line so far as spectral properties ar…

离散变量的正交多项式与Dirichlet核的有界性

Orthogonal polynomials of discrete variable and boundedness of Dirichlet kernel

对于系数指数衰减的紧Jacobi矩阵所定义的正交多项式，给出了正交性测度的精确性质。这允许显示均匀有界的正交展开式的部分和关于$L^\infty$规范，推广了类似的结果，小$q$ -Legendre，小$q$ -Jacobi和小$q$ -Laguerre多项式，作者。

Orthogonally additive polynomials on convolution algebras associated with a compact group

Let $G$ be a compact group, let $X$ be a Banach space, and let $P\colon L^1(G)\to X$ be an orthogonally additive, continuous $n$-homogeneous polynomial. Then we show that there exists a unique continuous linear map $Φ\colon L^1(G)\to X$ such that $P(f)=Φ\bigl(f\ast\stackrel{n}{\cdots}\ast f \bigr)$ for each $f\in L^1(G)$. We also seek analogues of this result about $L^1(G)$ for various other convolution algebras, including $L^p(G)$, for $1< p\le\infty$, and $C(G)$.

多个非交换变量的正交多项式。II

Orthogonal polynomials in several non-commuting variables. II

本文继续研究了一类Hankel型正定核的正交多项式性质。本文的主要结果是关于这类核的结构。