The spectral analysis of Frobenius-Perron operators
type: Item
instance of: scholarly article
title: The spectral analysis of Frobenius-Perron operators
zbMATH Open document ID: 0830.47022
author: J. Ding
author: Qiang Du
author: Tien-Yien Li
published in: Journal of Mathematical Analysis and Applications
publication date: 1994-10-10T00:00:00Z
review text: It is known that the Frobenius-Perron operator \(P_S: L^1(0, 1)\to L^1(0, 1)\) associated with a transformation \(S\) from \([0, 1]\) to itself with \(\inf|S'|> 1\) is quasi-compact as an operator on the Banach space \(BV[0, 1]\) of functions of bounded variation in \(L^1(0, 1)\), and thus \(P_S: BV[0, 1]\to BV[0, 1]\) possesses only the finite peripheral spectrum and in particular \(1\) is an isolated eigenvalue of \(P_S\). In this paper, the authors show that under mild conditions on \(S\), the spectrum of \(P_S: L^1(X)\to L^1(X)\) is either the closed unit disk \(\{\lambda\in \mathbb{C}: |\lambda|\leq 1\}\) or a cyclic subset of \(\{\lambda\in \mathbb{C}: |\lambda|= 1\}\).
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 635924
zbMATH Keywords: Frobenius-Perron operator
zbMATH Keywords: spectrum
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1200
OpenAlex ID: W2078360588
DOI: 10.1006/JMAA.1994.1200
description: scientific article; zbMATH DE number 635924