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We develop cohomological interpretations for several types of automorphicforms for Hecke triangle groups of infinite covolume. We then use theseinterpretations to establish explicit isomorphisms between spaces ofautomorphic forms, cohomology spaces and spaces of eigenfunctions of transferoperators. These results show a deep relation between spectral entities ofHecke surfaces of infinite volume and the dynamics of their geodesic flows.

Eigenfunctions of transfer operators and automorphic forms for Hecke triangle groups of infinite covolume