Mathematica Bohemica, Vol. 142, No. 2, pp. 113-124, 2017

Weighted Frobenius-Perron operators and their spectra

Mohammad Reza Jabbarzadeh, Rana Hajipouri

Received December 15, 2015.   First published November 22, 2016.

Mohammad Reza Jabbarzadeh, Rana Hajipouri, Department of Pure Mathematics, Faculty of Mathematical Sciences, and Research Institute for Fundamental Sciences, University of Tabriz, 29 Bahman Blvd, P. O. Box 51664, Tabriz, 5166616471, Iran, e-mail: mjabbar@tabrizu.ac.ir, r.hajipouri@tabrizu.ac.ir

Abstract: First, some classic properties of a weighted Frobenius-Perron operator $\mathcal{P}_\varphi^u$ on $L^1(\Sigma)$ as a predual of weighted Koopman operator $W=uU_\varphi$ on $L^\infty(\Sigma)$ will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of $\mathcal{P}_\varphi^u$ under certain conditions.

Keywords: Frobenius-Perron operator; Fredholm operator; spectrum

Classification (MSC 2010): 47B20, 47B38, 11Y50

DOI: 10.21136/MB.2016.0079-15

Full text available as PDF.


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