Analytic continuation and resonance-free regions for Sturm-Liouville pote ntials with power decay

Details Analytic continuation and resonance-free regions for Sturm-Liouville pote ntials with power decay Analytic continuation and resonance-free regions for Sturm-Liouville pote ntials with power decay

2000-06-08

arxiv.org/abs/math/0006064v1

Mathematics

Spectral Theory

Scientific paper

We are concerned with the Sturm-Liouville problem on the half line. We show
that when the potential $q$ is subject only to power decay at infinity the
$L^2$ solution may be continued into a sector of the so-called un-physical
sheet. This gives rise to resonance free regions and the numerical estimation
of resonances outside these regions.

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