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A criterion for Hill operators to be spectral operators of scalar type [PDF]

open access: yesJournal d'Analyse Mathématique, 2006
We derive necessary and sufficient conditions for a Hill operator (i.e., a one-dimensional periodic Schrö dinger operator) H = −d2/dx2 + V to be a spectral operator of scalar type.
F. Gesztesy, V. Trachenko
semanticscholar   +3 more sources

Scalar-type spectral operators and holomorphic semigroups

open access: yesSemigroup Forum, 1986
We show that a linear operator (possibly unbounded), A, on a reflexive Banach space, X, is a scalar-type spectral operator, with non-negative spectrum, if and only if the following conditions hold. (1) A generates a uniformly bounded holomorphic semigroup \(\{e^{- zA}\}_{Re(z)\geq 0}.\) (2) If \(F_ N(s)\equiv \int^{N}_{-N}\frac{\sin (sr)}{r}e^{irA}dr\),
R. Laubenfels
semanticscholar   +3 more sources
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