论文标题
Koopman和Perron-Frobenius运营商在复制内核Banach空间
Koopman and Perron-Frobenius Operators on reproducing kernel Banach spaces
论文作者
论文摘要
如今，Koopman和Perron-Frobenius操作员在科学领域的许多领域都越来越流行。 Koopman操作员的属性本质上取决于其作用的功能空间的选择。尤其是复制核希尔伯特空间（RKHSS）的情况在数据科学中引起了越来越多的关注。在本文中，我们为Koopman和Perron-Frobenius Operators提供了一个一般框架，用于再现内核Banach空间（RKBSS）。更确切地说，我们将这些运算符的基本已知属性从RKHSS扩展到RKBS，并在这些操作员的RKBS上使用离散和连续的时间系统上的这些操作员，包括对称和稀疏概念，包括对称和稀疏概念。
Koopman and Perron-Frobenius operators for dynamical systems have been getting popular in a number of fields in science these days. Properties of the Koopman operator essentially depend on the choice of function spaces where it acts. Particularly the case of reproducing kernel Hilbert spaces (RKHSs) draws more and more attention in data science. In this paper, we give a general framework for Koopman and Perron-Frobenius operators on reproducing kernel Banach spaces (RKBSs). More precisely, we extend basic known properties of these operators from RKHSs to RKBSs and state new results, including symmetry and sparsity concepts, on these operators on RKBS for discrete and continuous time systems.
