Smoothness of Hill's potential and lengths of spectral gaps

Vladimir Mikhailets, Volodymyr Molyboga

Let ${{\gamma }_q(n)}_{n\in \mathbb{N}}$ be the lengths of spectral gaps in a continuous spectrum of the Hill-Schrödinger operators S(q)u=-u''+q(x)u,\quad x\in \mathbb{R}, with 1-periodic…