89 citations · 1.1k across the 43 of their papers we have counts for
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math.AP2012★ 4 cited
Fractal Weyl laws for asymptotically hyperbolic manifolds
Kiril Datchev, Semyon Dyatlov
For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal upper bound on the number of resonances near the essential spectrum, with power determined b…
math.AP2012
Microlocal limits of plane waves and Eisenstein functions
Semyon Dyatlov, Colin Guillarmou
We study microlocal limits of plane waves on noncompact Riemannian manifolds (M,g) which are either Euclidean or asymptotically hyperbolic with curvature -1 near infinity. The plan…
math.AP2012★ 18 cited
Quantum ergodicity for restrictions to hypersurfaces
Semyon Dyatlov, Maciej Zworski
Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is…