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

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

2005-06-08

arxiv.org/abs/math/0506138v2

Mathematics

Spectral Theory

38 pages

Scientific paper

We 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.

Affiliated with

Also associated with

No associations

Rating

On the spectrum of Jacobi operators with quasi-periodic algebro-geometric coefficients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the spectrum of Jacobi operators with quasi-periodic algebro-geometric coefficients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the spectrum of Jacobi operators with quasi-periodic algebro-geometric coefficients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-538710