 05205 Vladimir Batchenko and Fritz Gesztesy
 On the spectrum of Jacobi operators with quasiperiodic algebrogeometric
coefficients
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Jun 8, 05

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Abstract. We characterize the spectrum of onedimensional Jacobi operators
H=aS^{+}+a^{}S^{}+b in l^{2}(\Z) with quasiperiodic
complexvalued algebrogeometric 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.
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