Bethe-Sommerfeld property of periodic and almost-periodic Schrödinger operators: results old and new
I will give a survey of situations when we can establish a Bethe-Sommerfeld property (that all large energies belong to the spectrum) for multidimensional Schrodinger operators with periodic and almost-periodic potentials. While in the periodic setting the results are more than ten years old, there has been a substantial recent activity in the almost-periodic case. In particular, I will describe my recent joint result with Yu. Karpeshina and R. Shterenberg.