Parameters associated with bivariate Bernstein-Szego measures on the bi-circle

On a two variable class of Bernstein-Szego measures

The one variable Bernstein-Szego theory for orthogonal polynomials on the real line is extended to a class of two variable measures. The polynomials orthonormal in the total degree ordering and the lexicographical ordering are constructed and their recurrence coefficients discussed.

On the approximation properties of bivariate $(p, q)-$Bernstein operators

In the present study, we have given a corrigendum to our paper on the approximation properties of bivariate $(p, q)-$Bernstein operators. Recently, we \cite{kar} have defined the bivariate $(p, q)-$Bernstein operators. Later, we have aware of Acar et. al \cite{acar} already have given some moments. In this case, we have revised \cite[Lemma 2.3]{kar}.

Orthogonality relations for bivariate Bernstein-Szegő measures

The orthogonality properties of certain subspaces associated with bivariate Bernstein-Szegő measures are considered. It is shown that these spaces satisfy more orthogonality relations than expected from the relations that define them. The results are used to prove a Christoffel-Darboux like formula for these measures.

Bernstein-Szegő measures, Banach algebras, and scattering theory

We give a simple and explicit description of the Bernstein-Szego type measures associated with Jacobi matrices which differ from the Jacobi matrix of the Chebyshev measure in finitely many entries. We also introduce a class of measures M which parametrizes the Jacobi matrices with exponential decay and for each element in M we define a scattering function. Using Banach algebras associated with increasing Beurling weights, we prove that the exponential decay of the coefficients in a Jacobi matrix is completely determined by the decay of the negative Fourier coefficients of the scattering functi…

通过有限正交关系构造伯恩斯坦-齐格勒多项式求积规则

Quadrature rules from finite orthogonality relations for Bernstein-Szego polynomials

本文通过将两种伯恩斯坦-齐格勒多项式家族结合，构建了关联有限维雅可比矩阵的特征基，从而得到该复合特征基的有限正交关系，进而推导出若干类似高斯的求积规则，用于精确积分有指定极点的有理函数。

平面上的Bernstein-Szegő测度

Bernstein-Szegő measures in the plane

本文定义了一类平面上的Bernstein-Szegő测度，利用Fejér-Riesz分解和Szegő映射的二维推广，建立了其谱性质并给出了有限矩刻画。