Resonances for non-analytic potentials

Details Resonances for non-analytic potentials Resonances for non-analytic potentials

2008-05-12

arxiv.org/abs/0805.1596v1

Mathematics

Spectral Theory

33 pages, 1 figure

Scientific paper

We consider semiclassical Schroedinger operators on R^n, with C^\infty potentials decaying polynomially at infinity. The usual theories of resonances do not apply in such a non-analytic framework. Here, under some additional conditions, we show that resonances are invariantly defined up to any power of their imaginary part. The theory is based on resolvent estimates for families of approximating distorted operators with potentials that are holomorphic in narrow complex sectors around R^n.

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