Report
Preservation of absolutely continuous spectrum of periodic Jacobi operators under perturbations of square--summable variation
| العنوان: | Preservation of absolutely continuous spectrum of periodic Jacobi operators under perturbations of square--summable variation |
|---|---|
| المؤلفون: | Kaluzhny, U., Shamis, M. |
| سنة النشر: | 2009 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Spectral Theory, Mathematical Physics |
| الوصف: | 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. Comment: 18pp; revised version |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/0912.1142 |
| رقم الانضمام: | edsarx.0912.1142 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |