On the cyclic structure of the peripheral point spectrum of Perron-Frobenius operators
The Frobenius-Perron operator acting on integrable functions and the Koopman operator acting on essentially bounded functions for a given nonsingular transformation on the unit interval can be shown to have cyclic spectrum by referring to the theory of lattice homomorphisms on a Banach lattice. In...
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| Format: | Others |
| Language: | English en |
| Published: |
2008
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| Online Access: | http://hdl.handle.net/1828/1257 |
| Summary: | The Frobenius-Perron operator acting on integrable functions and the Koopman operator acting on essentially bounded functions for a given nonsingular transformation on the unit interval can be shown to have cyclic spectrum by referring to the theory of lattice homomorphisms
on a Banach lattice. In this paper, it is verified directly that the peripheral
point spectrum of the Frobenius-Perron operator and the point spectrum of the Koopman operator are fully cyclic. Under
some restrictions on the underlying transformation, the Frobenius-Perron operator is known to be a well defined linear operator on
the Banach space of functions of bounded variation. It is also shown that the peripheral point spectrum of the Frobenius-Perron operator on the functions of bounded variation is fully cyclic. |
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