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

B. M. Brown; M. S. P. Eastham

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arXiv · math/0006064

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

B. M. Brown·M. S. P. Eastham

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Abstract

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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BibTeX RIS

B. M. Brown, M. S. P. Eastham. 2000-06-08. Analytic continuation and resonance-free regions for Sturm-Liouville pote ntials with power decay. https://arxiv.org/abs/math/0006064

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