Schrödinger operators with complex-valued potentials and no resonances

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dc.creatorChristiansen, T.
dc.date2004-08-26
dc.date.accessioned2026-07-07T04:31:25Z
dc.date.available2026-07-07T04:31:25Z
dc.descriptionIn dimension $d\geq 3$, we give examples of nontrivial, compactly supported, complex-valued potentials such that the associated Schrödinger operators have no resonances. If $d=2$, we show that there are potentials with no resonances away from the origin. These Schrödinger operators are isophasal and have the same scattering phase as the Laplacian on $\Real^d$. In odd dimensions $d\geq 3$ we study the fundamental solution of the wave equation perturbed by such a potential. If the space variables are held fixed, it is super-exponentially decaying in time.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0408052
dc.identifierhttp://arxiv.org/abs/math-ph/0408052
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57807
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject35P25; 47A40; 81U05; 58J50
dc.titleSchrödinger operators with complex-valued potentials and no resonances
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