Xin Zhao


Nanjing Universuty


Thursday, October 10, 2019 - 2:00pm to 3:00pm


rh 340p

In this talk, we first consider quasi-periodic Schr\"odinger operators with finitely differentiable potentials. If the potential is analytic, there are numerous results. But not every result holds if one replaces the analyticity with a smoothness condition. We will give some positive results in this aspect,  generalizing some interesting results in the analytic case to the finitely smooth case. This includes the global reducibility results, generalized Chamber's formula and their applications to the study of continuity of the spectra. Finally we will give a recent result on the continuity of spectral measure of multi frequency quasi-periodic Schr\"odinger operators with small analytic quasi-periodic potentials.