Essential Closures and AC Spectra for Reflectionless CMV, Jacobi, and Schrödinger Operators Revisited

Simple item page
dc.creatorGesztesy, Fritz
dc.creatorMakarov, Konstantin A.
dc.creatorZinchenko, Maxim
dc.date2008-03-21
dc.date.accessioned2026-07-07T09:27:54Z
dc.date.available2026-07-07T09:27:54Z
dc.descriptionWe provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of absolutely continuous measures. As an elementary application of the notion of the essential closure of subsets of $\bbR$ we revisit the fact that CMV, Jacobi, and Schrödinger operators, reflectionless on a set E of positive Lebesgue measure, have absolutely continuous spectrum on the essential closure of the set E (with uniform multiplicity two on E). Though this result in the case of Schrödinger and Jacobi operators is known to experts, we feel it nicely illustrates the concept and usefulness of essential closures in the spectral theory of classes of reflectionless differential and difference operators.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0803.3178
dc.identifierhttp://arxiv.org/abs/0803.3178
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157269
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject34B20, 34L05, 34L40; 34B24, 34B27, 47A10
dc.titleEssential Closures and AC Spectra for Reflectionless CMV, Jacobi, and Schrödinger Operators Revisited
dc.typetext

Files

Collections

arXiv