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A trace formula for resonances and applications to semi-classical Schrödinger operators. (English) Zbl 1061.35506

From the introduction: We explain a trace formula valid in all dimensions, and even for long-range perturbations of the Laplacian. The new trace-formula permits to recover most (and perhaps all) the lower bounds on the density of resonances near the real axis, for certain compactly supported perturbations of the Laplacian.

MSC:

35P25 Scattering theory for PDEs
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35J10 Schrödinger operator, Schrödinger equation
47F05 General theory of partial differential operators
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