Imbedded Singular Continuous Spectrum for Schrödinger Operators

Simple item page
dc.creatorKiselev, A.
dc.date2001-11-19
dc.date.accessioned2026-07-07T04:44:39Z
dc.date.available2026-07-07T04:44:39Z
dc.descriptionWe construct examples of potentials $V(x)$ satisfying $|V(x)| \leq \frac{h(x)}{1+x},$ where the function $h(x)$ is growing arbitrarily slowly, such that the corresponding Schrödinger operator has imbedded singular continuous spectrum. This solves one of the fifteen "twenty-first century" problems for Schrödinger operators posed by Barry Simon. The construction also provides the first example of a Schrödinger operator for which Möller wave operators exist but are not asymptotically complete due to the presence of singular continuous spectrum.
dc.description30 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0111200
dc.identifierhttp://arxiv.org/abs/math/0111200
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62678
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject34L40; 34L25; 81U05
dc.titleImbedded Singular Continuous Spectrum for Schrödinger Operators
dc.typetext

Files

Collections

arXiv