On Schur parameters in Steklov's problem

Randomized Verblunsky Parameters in Steklov's Problem

We consider randomized Verblunsky parameters for orthogonal polynomials on the unit circle as they relate to the problem of Steklov, bounding the polynomials' uniform norm independent of $n$.

特征函数、Schur参数与Schur函数的伪延拓

Characteristic Function, Schur Parameters and Pseudocontinuation of Schur functions

本文综述了利用Schur参数和特征函数方法研究Schur函数伪延拓性的关键结果，包括判据、模型构造及应用。

Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle

It is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five-diagonal matrices depending on the Schur parameters. This result is achieved through the study of orthogonal Laurent polynomials on the unit circle. More precisely, it is a consequence of the five term recurrence relation obtained for these orthogonal Laurent polynomials, and the one to one correspondence established between them and the orthogonal polynomials on the unit circle. As an application, some results relating the behavior of the zeros of orthogonal polynomials and the …

The Resolvent Matrix of the Truncated Hausdorff Matrix Moment Problem via New Dyukarev-Stieltjes Parameters and Extremal Solutions via Continued Fractions

We obtain a new multiplicative decomposition of the resolvent matrix of the truncated Hausdorff matrix moment (THMM) problem in the case of an odd and even number of moments via new Dyukarev-Stieltjes matrix (DSM) parameters. Explicit interrelations between new DSM parameters and orthogonal matrix polynomials on a finite interval $[a,b]$, as well as the Schur complements of the block Hankel matrices constructed through the moments of the THMM problem are given. Additionally, the extremal solutions of the THMM problem are represented via matrix continued fractions in terms of the DSM parameters…

正交多项式，Szego-Verblunsky定理与Baxter定理在四元数球面上的应用

Orthogonal Polynomials, a Szegő--Verblunsky Theorem and Baxter's Theorem on the Quaternionic Sphere

本文研究四元数单位球上的正交多项式理论，扩展了Szego递推关系、正交多项式零点定理、Szego-Verblunsky定理和Baxter定理，引入了Alpay等人提出的q-正测量概念及矩阵值Schur递推关系和Verblunsky公式。

On the class SI of J-contractive functions intertwining solutions of linear differential equations

In the PhD thesis of the second author under the supervision of the third author was defined the class SI of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative 2D systems invariant in one direction. In this paper we extend and solve in the class SI, a number of problems originally set for the class SC of functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned signature matrix J. The problems we consider include the Schur algorithm, the partial realization problem and t…