Asymptotics of instability zones of Hill operators with a two term potential

Abstract

We give a sharp asymptotics of the instability zones of the Hill operator L y = − y ″ + ( a cos 2 x + b cos 4 x ) y for arbitrary real a , b ≠ 0 . To cite this article: P. Djakov, B. Mityagin, C. R. Acad. Sci. Paris, Ser. I 339 (2004).