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Resonances for bottles and trace formulae. (English) Zbl 0979.35109
Author’s abstract: In the first half of the paper, we give a simplified proof of a recent local trace formula for resonances. In the second half we use similar ideas to study resonances near the real axis in bottle like situations. As to the previous results, see J. Sjöstrand and M. Zworski [Commun. Partial Differ. Equations 18, No. 5-6, 847-857 (1993; Zbl 0784.35070); J. Funct. Anal. 123, No. 2, 336-367 (1994; Zbl 0823.35137)]; J. Sjöstrand [NATO ASI Ser., Ser. C, Math. Phys. Sci. 490, 377-437 (1997; Zbl 0877.35090)]; M. Zworski [Asian J. Math. 2, No. 3, 609-618 (1998; Zbl 0932.47004)].

MSC:
35P15 Estimates of eigenvalues in context of PDEs
35P25 Scattering theory for PDEs
47A40 Scattering theory of linear operators
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