On the spectrum of Jacobi operators with quasi-periodic algebro-geometric coefficients

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dc.creatorBatchenko, Vladimir
dc.creatorGesztesy, Fritz
dc.date2005-06-08
dc.date2005-11-30
dc.date.accessioned2026-07-07T06:40:13Z
dc.date.available2026-07-07T06:40:13Z
dc.descriptionWe characterize the spectrum of one-dimensional Jacobi operators H=aS^{+}+a^{-}S^{-}+b in l^{2}(\Z) with quasi-periodic complex-valued algebro-geometric coefficients (which satisfy one (and hence infinitely many) equation(s) of the stationary Toda hierarchy) associated with nonsingular hyperelliptic curves. The spectrum of H coincides with the conditional stability set of H and can explicitly be described in terms of the mean value of the Green's function of H. As a result, the spectrum of H consists of finitely many simple analytic arcs in the complex plane. Crossings as well as confluences of spectral arcs are possible and discussed as well.
dc.description38 pages
dc.identifierhttps://arxiv.org/abs/math/0506138
dc.identifierhttp://arxiv.org/abs/math/0506138
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/101338
dc.subjectSpectral Theory
dc.subjectMathematical Physics
dc.subject34L05, 47B36, 35Q58, 35Q51
dc.titleOn the spectrum of Jacobi operators with quasi-periodic algebro-geometric coefficients
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