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.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/1257 |
| Date | 17 November 2008 |
| Creators | Sorge, Joshua |
| Contributors | Bose, Christopher |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Available to the World Wide Web |
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