Preservation of absolutely continuous spectrum of periodic Jacobi operators under perturbations of square--summable variation

Mathematics – Spectral Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

18pp; revised version

Scientific paper

We study self-adjoint bounded Jacobi operators of the form: (J \psi)(n) = a_n \psi(n + 1) + b_n \psi(n) +a_{n-1} \psi(n - 1) on $\ell^2(\N)$. We assume that for some fixed q, the q-variation of $\{a_n\}$ and $\{b_n\}$ is square-summable and $\{a_n\}$ and $\{b_n\}$ converge to q-periodic sequences. Our main result is that under these assumptions the essential support of the absolutely continuous part of the spectrum of J is equal to that of the asymptotic periodic Jacobi operator. This work is an extension of a recent result of S.A.Denisov.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Preservation of absolutely continuous spectrum of periodic Jacobi operators under perturbations of square--summable variation 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 Preservation of absolutely continuous spectrum of periodic Jacobi operators under perturbations of square--summable variation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Preservation of absolutely continuous spectrum of periodic Jacobi operators under perturbations of square--summable variation will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-242531

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.