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Register a new userZero is a resonance of every Schottky surface
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For certain spectral parameters we find explicit eigenfunctions of transfer operators for Schottky surfaces. Comparing the dimension of the eigenspace for the spectral parameter zero with the multiplicity of topological zeros of the Selberg zeta function, we deduce that zero is a resonance of every Schottky surface.
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When modeling game situations of incomplete information one usually considers the players hierarchies of beliefs, a source of all sorts of complications. Harsanyi (1967-68)s idea henceforth referred to as the Harsanyi program is that hierarchies of beliefs can be replaced by types. The types constitute the type space. In the purely measurable framework Heifetz and Samet (1998) formalize the concept of type spaces and prove the existence and the uniqueness of a universal type space. Meier (2001) shows that the purely measurable universal type space is complete, i.e., it is a consistent object. With the aim of adding the finishing touch to these results, we will prove in this paper that in the purely measurable framework every hierarchy of beliefs can be represented by a unique element of the complete universal type space.
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