For Parry-type beta-expansions, the Perron-Frobenius operator has eigenvalue 1 attracting Lipschitz functions exponentially in L1, while its point spectrum on L^p (1≤p≤2) contains the entire open unit disk.
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Spectral and dynamical results related to certain non-integer base expansions on the unit interval
For Parry-type beta-expansions, the Perron-Frobenius operator has eigenvalue 1 attracting Lipschitz functions exponentially in L1, while its point spectrum on L^p (1≤p≤2) contains the entire open unit disk.