High-Index Asymptotics of Mathieu Spectral Gaps and Splittings

Berkay Anahtarci

Consider the Mathieu operator $L=-d^2/d{x}^2+2a\cos (2x)$ for fixed $a\in \mathbb{C}\setminus \{0\}$. For large enough $n$, the periodic ($n$ even) or anti-periodic ($n$ odd) problem on…