Exponential Decay of Correlation Coefficients for Geodesic Flows
We obtain exponential decay bounds for correlation coefficients of geodesic flows on surfaces of constant negative curvature (and for all Riemannian symmetric spaces of rank one), answering a question posed by Marina Ratner. The square integrable functions on the unit sphere bundle of M are allowed to satisfy weak differentiability conditions. The methods are those of unitary representation theory and invoke the notion of Sobelev vectors of representations. In the course of the discussion we obtain a new characterization of tempered irreducible representation of semi-simple groups.
KeywordsIrreducible Representation Unitary Representation Borel Subgroup Maximal Compact Subgroup Geodesic Flow
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