We study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever the Banach space bounds L-infinity and the transformation fails to be Markov. Constructing a family of Banach spaces we show that the lower bound on the essential spectral radius is optimal. Indeed, these Banach spaces realise an essential spectral radius as close as desired to the theoretical best possible case.
Butterley, O.j., Canestrari, G., Jain, S. (2023). Discontinuities cause essential spectrum. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 398(2), 627-653 [10.1007/s00220-022-04531-6].
Discontinuities cause essential spectrum
Oliver Butterley;
2023-01-01
Abstract
We study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever the Banach space bounds L-infinity and the transformation fails to be Markov. Constructing a family of Banach spaces we show that the lower bound on the essential spectral radius is optimal. Indeed, these Banach spaces realise an essential spectral radius as close as desired to the theoretical best possible case.File in questo prodotto:
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