Intertwining the geodesic flow and the Schrodinger group on hyperbolic surfaces

Details Intertwining the geodesic flow and the Schrodinger group on hyperbolic surfaces Intertwining the geodesic flow and the Schrodinger group on hyperbolic surfaces

2010-10-05

arxiv.org/abs/1010.0867v1

Mathematics

Spectral Theory

Scientific paper

We construct an explicit intertwining operator $\lcal$ between the Schr\"odinger group $e^{it \frac\Lap2} $ and the geodesic flow $g^t$ on certain Hilbert spaces of symbols on the cotangent bundle $T^* \X$ of a compact hyperbolic surface $\X = \Gamma \backslash \D$. Thus, the quantization Op(\lcal^{-1} a) satisfies an exact Egorov theorem. The construction of $\lcal$ is based on a complete set of Patterson-Sullivan distributions.

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