论文标题
在多芯片分析上，一种非交通性的De Branges-Rovnyak空间和Schur分析的方法
On a polyanalytic a approach to noncommutative de Branges-Rovnyak spaces and Schur analysis
论文作者
论文摘要
在本文中，我们开始研究Fueter超晶函数框架中Schur分析和De Branges-Rovnyak空间。与其他方法的不同之处在于，我们考虑了由appell样多项式跨越的函数类别。从各种观点（例如在操作者理论中），这种方法非常有效，并允许与最近开发的切片多序函数理论建立联系。 我们解决了许多问题：我们描述了一个耐寒的空间，Schur乘数和相关结果。我们还讨论了Blaschke功能，Herglotz乘数及其相关的内核和Hilbert空间。最后，我们考虑了半个空间案例的对应物，以及相应的耐寒空间，Schur乘数和Carathéodory乘数。
In this paper we begin the study of Schur analysis and de Branges-Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like polynomials. This approach is very efficient from various points of view, for example in operator theory, and allows to make connections with the recently developed theory of slice polyanalytic functions. We tackle a number of problems: we describe a Hardy space, Schur multipliers and related results. We also discuss Blaschke functions, Herglotz multipliers and their associated kernels and Hilbert spaces. Finally, we consider the counterpart of the half-space case, and the corresponding Hardy space, Schur multipliers and Carathéodory multipliers.
