Spectral properties of a class of operators associated with maps in one dimension
1991 ◽
Vol 11
(4)
◽
pp. 757-767
◽
Keyword(s):
AbstractLet f be a piecewise monotone map of the interval [0,1] to itself, and g a function of bounded variation on [0, 1]. Hofbauer, Keller and Rychlik have studied operators on functions of bounded variation, whereAmong other things, they show that the essential spectral radius of is in many cases strictly smaller than the spectral radius; there exist therefore isolated eigenvalues of finite multiplicity. The purpose of the present paper is to prove similar results for a more general class of operators forming an algebra (and therefore containing sums of operators like ). An analogous extension was presented by Ruelle for operators associated with expanding maps.
1948 ◽
Vol 44
(1)
◽
pp. 8-12
◽
1964 ◽
Vol 16
◽
pp. 479-484
◽
1965 ◽
Vol 14
(3)
◽
pp. 211-219
◽
2017 ◽
Vol 147
(3)
◽
pp. 449-503
◽