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Resonances in physics and geometry. (English) Zbl 1177.58021

Summary: For a broad range of phenomena, a state can be described by two parameters, rest energy and rate of decay. This information is encoded in a complex number whose real part is the energy and imaginary part is the rate of decay. Mathematically it appears as a pole of a natural meromorphic operator and is called a resonance. This article motivates the study of resonances and describes some recent advances in this study.

MSC:

58J50 Spectral problems; spectral geometry; scattering theory on manifolds
58J37 Perturbations of PDEs on manifolds; asymptotics
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