Improved asymptotics of the spectral gap for the Mathieu operator

Berkay Anahtarci, Plamen Djakov

The Mathieu operator {equation*} L(y)=-y"+2a \cos{(2x)}y, \quad a\in \mathbb{C},\;a\neq 0, {equation*} considered with periodic or anti-periodic boundary conditions has, close to $…