Proves quantum ergodicity for subLaplacians on contact metric manifolds with ergodic Reeb flow via adapted semiclassical calculus and microlocal projectors.
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A pseudodifferential calculus is built on filtered manifolds via local quantization of operator-valued symbols on osculating group duals, with proofs of composition, adjoint, parametrices and Sobolev continuity, coinciding with the van Erp-Yuncken groupoid calculus in the polyhomogeneous case.
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Quantum ergodicity for contact metric structures
Proves quantum ergodicity for subLaplacians on contact metric manifolds with ergodic Reeb flow via adapted semiclassical calculus and microlocal projectors.
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Quantization on filtered manifolds
A pseudodifferential calculus is built on filtered manifolds via local quantization of operator-valued symbols on osculating group duals, with proofs of composition, adjoint, parametrices and Sobolev continuity, coinciding with the van Erp-Yuncken groupoid calculus in the polyhomogeneous case.