控制多项式的因式分解定理

控制空间与线性和多线性求和算子的因式分解

Domination spaces and factorization of linear and multilinear summing operators

众所周知，不是每个非线性算子的可和性都能导出因子分解定理。在本文中，我们进行了详细的研究，因式分解计划求和线性和非线性算子。我们的目标是整合在同一理论下的广泛的家庭类映射的Pietsch型分解定理。我们分析了一类线性算子定义的可和性不等式涉及齐次映射。我们的构造包括绝对$p$ -求和线性算子，$(p,σ)$ -绝对连续线性算子，可分解强$p$ -求和多重线性算子，$(p_1,\ldots,p_n)$ -支配多重线性算子和支配$(p_1,\ldots, p_n;σ)$ -连续多重线性算子的情形.

Quadratic transformation and matrix biorthogonal polynomials: an $\mathcal{LU}$ factorization approach

The manuscript presents the $LU$ approach to matrix biorthogonal polynomials when all the even ordered entries in the Gram matrix are zero. This arises in case of a quadratic transformation which is briefly discussed. Further, the main diagonal of the Gram matrix is a zero diagonal and we present the theory that follows from this fact. Precisely, we discuss the Christoffel transformation and matrix representations of the kernel polynomials, usually called the ABC Theorem. Finally, we provide an illustration of our results assuming the Gram matrix has Hankel symmetry.

Spectral Factorization and Entire Functions

The Fejér-Riesz spectral factorization lemma, which represents a nonnegative trigonometric polynomial as the squared modulus of a trigonometric polynomial, was extended by Ahiezer to factorize certain entire functions and by Helson and Lowdenslager to factorize certain functions on compact connected abelian groups whose Pontryagin duals are equipped with a linear order. This paper relates these factorizations for archimedian orders using the theory of almost periodic functions.

infinite dimensional空间上的控制多项式

Dominated polynomials on infinite dimensional spaces

本文的目的是证明任意无限维巴拿赫空间上存在非支配标量值m-齐次多项式（m>=3）的猜想的一个更强的版本.

Spectral theory for bounded banded matrices with positive bidiagonal factorization and mixed multiple orthogonal polynomials

Spectral and factorization properties of oscillatory matrices leads to a spectral Favard theorem for bounded banded matrices, that admit a positive bidiagonal factorization, in terms of sequences of mixed multiple orthogonal polynomials with respect to a set positive Lebesgue-Stieltjes measures. A mixed multiple Gauss quadrature formula with corresponding degrees of precision is given.

Fejér-Riesz分解与双圆上正交二元多项式的结构

Fejér-Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle

本文给出了双圆上正三角多项式Q（θ，θ）的一个完整刻画，它可分解为Q（θ，θ）=| p（e^{iθ}，e^{i θ}）|其中p（z，w）是|z| =1且|w| \leq 1的非零多项式。这些条件是根据与双圆上关于权重1/（4π^2Q（θ，θ））正交的字典序和逆字典序的多项式相关联的递归系数。我们使用这个结果来描述如何具体的分解的双圈的权重可以被翻译成相关的相应的多项式的递归系数的身份，反之亦然。特别是，我们刻画了双圆上的Borel测度，其中系数乘以与两个算子相关的逆多项式：在字典序中乘以z和在逆字典序中乘以w在特定点之后消失。这可以被认为是一个谱型结果，类似于单位圆上Bernstein-SzegIgn测度的特征。