论文标题
离散的分析功能，结构化矩阵和新的时刻问题家族
Discrete analytic functions, structured matrices and a new family of moment problems
论文作者
论文摘要
使用Zeilberger生成函数公式用于象限中离散分析函数的值，我们与结构化重现内核空间，结构化矩阵和广义力矩问题的理论建立联系。在起源附近，Dijksma，Langer和de Snoo的功能分析的结果是凯林空间实现的结果。一个关键的观察结果是，使用简单的Moebius变换，可以将右上象限中离散分析功能的研究减少到开放单元磁盘中功能理论问题。例如，我们将每个有限的阳性度量与$ [0,2π] $上的每个有限级度量相关联，在右上方四分之一平面上具有离散的分析函数，其值在晶格上定义了一个正定函数。重点是理性案例，这两者都在基本的carathéodory函数是理性的，并且在积极的情况下，光谱函数是理性的。理性案例和一般情况是通过统一扩张而链接的
Using Zeilberger generating function formula for the values of a discrete analytic function in a quadrant we make connections with the theory of structured reproducing kernel spaces, structured matrices and a generalized moment problem. An important role is played by a Krein space realization result of Dijksma, Langer and de Snoo for functions analytic in a neighborhood of the origin. A key observation is that, using a simple Moebius transform, one can reduce the study of discrete analytic functions in the upper right quadrant to problems of function theory in the open unit disk. As an example, we associate to each finite positive measure on $[0,2π]$ a discrete analytic function on the right-upper quarter plane with values on the lattice defining a positive definite function. Emphasis is put on the rational case, both when an underlying Carathéodory function is rational and when, in the positive case, the spectral function is rational. The rational case and the general case are linked via the existence of a unitary dilation, possibly in a Krein space
