A Criterion for Hill Operators to be Spectral Operators of Scalar Type

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dc.creatorGesztesy, Fritz
dc.creatorTkachenko, Vadim
dc.date2006-10-17
dc.date.accessioned2026-07-07T07:29:08Z
dc.date.available2026-07-07T07:29:08Z
dc.descriptionWe derive necessary and sufficient conditions for a Hill operator (i.e., a one-dimensional periodic Schrödinger operator) $H=-d^2/dx^2+V$ to be a spectral operator of scalar type. The conditions show the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential $V$. In the course of our analysis we also establish a functional model for periodic Schrödinger operators that are spectral operators of scalar type and develop the corresponding eigenfunction expansion. The problem of deciding which Hill operators are spectral operators of scalar type appears to have been open for about 40 years.
dc.description52 pages
dc.identifierhttps://arxiv.org/abs/math/0610502
dc.identifierhttp://arxiv.org/abs/math/0610502
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/117986
dc.subjectSpectral Theory
dc.subjectFunctional Analysis
dc.subject34B30, 47B40, 47A10
dc.titleA Criterion for Hill Operators to be Spectral Operators of Scalar Type
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