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Semi-classical estimates for the resolvent in nontrapping geometries. (English) Zbl 1161.81368

Summary: The purpose of this note is to present a very natural and simple method to prove (for nontrapping geometries) the existence of resonance-free regions and to give estimates for the resolvent in these regions. The method is valid in any dimensions of space and does not rely on Lax and Phillips theory.

MSC:

81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
47A40 Scattering theory of linear operators
47F05 General theory of partial differential operators
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