Mathematics – Spectral Theory
Scientific paper
2009-06-18
Mathematics
Spectral Theory
Scientific paper
We investigate the spectral properties of Schr\"odinger operators in l^2(Z) with limit-periodic potentials. The perspective we take was recently proposed by Avila and is based on regarding such potentials as generated by continuous sampling along the orbits of a minimal translation of a Cantor group. This point of view allows one to separate the base dynamics and the sampling function. We show that for any such base dynamics, the spectrum is a Cantor set of positive Lebesgue measure and purely absolutely continuous for a dense set of sampling functions, and it is a Cantor set of zero Lebesgue measure and purely singular continuous for a dense G_\delta set of sampling functions.
Damanik David
Gan Zheng
No associations
LandOfFree
Spectral Properties of Limit-Periodic Schrödinger Operators 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 Spectral Properties of Limit-Periodic Schrödinger Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral Properties of Limit-Periodic Schrödinger Operators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-725415