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math.SP2012★ 23 cited
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…
math.SP2011★ 21 cited
Inverse problems in spectral geometry
Kiril Datchev, Hamid Hezari
In this survey we review positive inverse spectral and inverse resonant results for the following kinds of problems: Laplacians on bounded domains, Laplace-Beltrami operators on co…