27 citations · 211 across the 28 of their papers we have counts for
5 papers · 1 filter
Approximation and equidistribution of phase shifts: spherical symmetry
Kiril Datchev, Jesse Gell-Redman, Andrew Hassell +1
Consider a semiclassical Hamiltonian \begin{equation*} H_{V, h} := h^{2} Δ+ V - E \end{equation*} where is a semiclassical parameter, is the positive Laplacian on $\mat…
Resonance free regions for nontrapping manifolds with cusps
Kiril Datchev
We prove resolvent estimates for nontrapping manifolds with cusps which imply the existence of arbitrarily wide resonance free strips, local smoothing for the Schrodinger equation,…
Sharp polynomial bounds on the number of Pollicott-Ruelle resonances
Kiril Datchev, Semyon Dyatlov, Maciej Zworski
We give a sharp polynomial bound on the number of Pollicott-Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in expansions of correlat…
Semiclassical resolvent estimates at trapped sets
Kiril Datchev, András Vasy
We extend our recent results on propagation of semiclassical resolvent estimates through trapped sets when a priori polynomial resolvent bounds hold. Previously we obtained non-tra…
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…