On the spectrum of Frobenius-Perron operators
The spectrum of the Frobenius-Perron operator \(P: L^1 \to L^1\) associated to nonsingular transformations on \(\sigma\)-finite measure spaces is studied. It was conjectured that the spectrum \(\sigma(P)\) of \(P\) is either the unit disc or a cyclic subset of the union of the unit circle and \(0\). The author proves this conjecture in some cases which are more general than those in previous works.
scientific article; zbMATH DE number 1542468