Journal of Spectral Theory


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Volume 5, Issue 3, 2015, pp. 599–615
DOI: 10.4171/JST/108

Published online: 2015-08-28

Resonances and lower resolvent bounds

Kiril Datchev[1], Semyon Dyatlov[2] and Maciej Zworski[3]

(1) Massachusetts Institute of Technology, Cambridge, USA
(2) Massachusetts Institute of Technology, Cambridge, USA
(3) University of California, Berkeley, USA

We show how the presence of resonances close to the real axis implies exponential lower bounds on the norm of the cut-off resolvent on the real axis.

Keywords: Resolvent estimates, scattering resonances, semiclassical analysis

Datchev Kiril, Dyatlov Semyon, Zworski Maciej: Resonances and lower resolvent bounds. J. Spectr. Theory 5 (2015), 599-615. doi: 10.4171/JST/108