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Keywords:
Frobenius-Perron operator; Fredholm operator; spectrum
Frobenius-Perron operator; Fredholm operator; spectrum
Summary:
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.
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