Transfer operators of piecewise expanding maps have essential spectral radius at least 1/k or 1/Θ∞(1−s) whenever the Banach space contains interval indicators with natural norm bounds.
Transfer operators, atomic decomposition and the Bestiary
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Arbieto and S. recently used atomic decomposition to study transfer operators. We give a long list of old and new expanding dynamical systems for which those results can be applied, obtaining the quasi-compactness of transfer operator acting on Besov spaces of measure spaces with a good grid.
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Discontinuous observables as an obstruction for small essential spectral radius
Transfer operators of piecewise expanding maps have essential spectral radius at least 1/k or 1/Θ∞(1−s) whenever the Banach space contains interval indicators with natural norm bounds.