Traceformula for Resonances in Small Domains

Traceformulas are useful in the study of resonances. In this article, we work in a semi-classical black box framework and obtain a traceformula of the same type as that of the second author, now for the resonances in h-dependent domains of size h, and under somewhat more restrictive assumptions. As an application, we extend to a long range situation a result by V. Petkov and M. Zworski on Breit–Wigner peaks in the scattering phase.