Orthogonality relations for bivariate Bernstein-Szegő measures

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。

Bernstein-Szegő measures on the two dimensional torus

We present a new viewpoint (namely, reproducing kernels) and new proofs for several recent results of J. Geronimo and H. Woerdeman on orthogonal polynomials on the two dimenional torus (and related subjects). In addition, we show how their results give a new proof of Ando's inequality via an equivalent version proven by Cole and Wermer. A simple necessary and sufficient condition for two variable polynomial stability is also given.

Bivariate Bernstein-gamma functions and moments of exponential functionals of subordinators

In this paper, we extend recent work on the functions that we call Bernstein-gamma to the class of bivariate Bernstein-gamma functions. In the more general bivariate setting, we determine Stirling-type asymptotic bounds which generalise, improve upon and streamline those found for the univariate Bernstein-gamma functions. Then, we demonstrate the importance and power of these results through an application to exponential functionals of Lévy processes. In more detail, for a subordinator (a non-decreasing Lévy process) $(X_s)_{s\geq 0}$, we study its \textit{exponential functional}, $\int_0^t e^…

Bernstein-Markov测度与Toeplitz理论

Bernstein-Markov measures and Toeplitz theory

本文证明在赋予大线丛的紧复流形上，与Bernstein-Markov测度关联的Toeplitz算子在复合下构成代数，并基于Bergman核非对角渐近分析推导出Szegő型谱等分布结果。