Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions

We determine the spectra of composition operators acting on weighted Banach spaces of analytic functions on the unit disc defined for a radial weight v, when the symbol of the operator has a fixed point in the open unit disc. We also investigate in this case the growth rate of the Koenigs eigenfunction and its relation with the essential spectral radius of the composition operator.