Bibliographic Details
| Title: |
Spectral approximation for ergodic CMV operators with an application to quantum walks. |
| Authors: |
Fillman, Jake1 fillman@vt.edu, Ong, Darren C.2 darrenong@xmu.edu.my, VandenBoom, Tom3 tv4@rice.edu |
| Source: |
Journal of Mathematical Analysis & Applications. Nov2018, Vol. 467 Issue 1, p132-147. 16p. |
| Subjects: |
Common method variance, Lyapunov exponents, Schrödinger equation, Spectral theory, Approximation theory |
| Abstract: |
We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices. We proceed by proving several variational estimates on the measure of the spectrum and the vanishing set of the Lyapunov exponent for CMV matrices, which represent CMV analogues of results obtained for Schrödinger operators due to Y. Last in the early 1990s. Having done so, we combine those estimates with results from inverse spectral theory to obtain purely absolutely continuous spectrum. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
