Resumen de Spectral gaps of the Schrödinger operators with periodic d'-interactions and Diophantine approximations
We study the spectral gaps of the Schrödinger operator where ?(0,2p) and are parameters. Let t=2p-?. Suppose that the ratio ?0:=t/? is irrational. We denote the jth gap of the spectrum of H by Gj, its length by |Gj|. We obtain a relationship between the asymptotic behaviour of |Gj| as j?8 and the Diophantine properties of ?0. In particular, we show that if ß1+ß2=0, then where M(?0) stands for the Markov constant of ?0
