Weighted Frobenius-Perron and Koopman operators
type: Item
instance of: scholarly article
title: Weighted Frobenius-Perron and Koopman operators
zbMATH Open document ID: 1203.47018
author: B. E. Eshmatov
published in: Bulletin of the Iranian Mathematical Society
publication date: 2010-06-07T00:00:00Z
review text: The author introduces operators \({\mathcal P}^u_\varphi: L_1 \to L_1\), \({\mathcal P}^u_\varphi= P_\varphi M_u\) and \(M_uU_\varphi: L_\infty \to L_\infty\), where \(P_\varphi\) and \(U_\varphi\) are the classical Frobenius-Perron and Koopman operators, respectively, and \(M_u\) is the corresponding multiplication operator. In other words, \({\mathcal P}^u_\varphi\) is defined by means of the equation \(\int_A {\mathcal P}^u_\varphi f \,d\mu = \int_{\varphi^{-1}(A)} u f \,d\mu\), \(A \in \Sigma\), and \(U_\varphi\) is defined by \(U_\varphi f = f \circ\varphi\). The author studies conditions under which \({\mathcal P}^u_\varphi\) and \(M_uU_\varphi\) are well-defined, bounded, have closed range, or are compact.
reviewed by: Vladimir Kadets
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 5716973
zbMATH Keywords: Frobenius-Perron operator
zbMATH Keywords: Koopman operator
zbMATH Keywords: conditional expectation operator
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5716973