The Spectral Analysis of Frobenius Perron Operators
Document Type
Article
Publication Date
6-1-1994
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
It is known that the Frobenius-Perron operator Ps:L1(0,1)→L1(0,1) associated with a transformation S from [0,1] to itself with inf|S′|>1 is quasi-compact as an operator on the Banach space BV[0,1] of functions of bounded variation in L1(0,1), and thus Ps: BV[0,1]→BV[0,1] possesses only the finite peripheral spectrum and in particular 1 is an isolated eigenvalue of Ps. In this paper, we show that under mild conditions on S, the spectrum of Ps:L1(X)→L1(X) is either the closed unit disk {λϵC:|λ|≤1} or a cyclic subset of {λϵC:|λ|=1}.
Publication Title
Journal of Mathematical Analysis and Applications
Volume
184
Issue
2
First Page
285
Last Page
301
Recommended Citation
Ding, J.,
Du, Q.,
Li, T.
(1994). The Spectral Analysis of Frobenius Perron Operators. Journal of Mathematical Analysis and Applications, 184(2), 285-301.
Available at: https://aquila.usm.edu/fac_pubs/7265