Discontinuities cause essential spectrum
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Publication:6400132
DOI10.1007/S00220-022-04531-6arXiv2205.12607MaRDI QIDQ6400132
Sakshi Jain, Oliver Butterley, Giovanni Canestrari
Publication date: 25 May 2022
Abstract: We study transfer operators associated to piecewise monotone interval transformations and show that the essential spectrum is large whenever the Banach space bounds 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.
Dynamical systems involving maps of the interval (37E05) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Random iteration (37H12)
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