  The Hill operator admits a band gap structure. As a special case, like the
Mathieu operator, one has only open gaps, however, the instability intervals of
the Whittaker-Hill operator may be open or closed. In 2007, P. Djakov and B.
Mityagin gave the asymptotics of band gaps for a special Whittaker-Hill
operator [P. Djakov and B. Mityagin, J. Funct. Anal., 242, 157-194 (2007).]. In
this paper, a more general Whittaker-Hill operator is considered and the
asymptotics of the instability intervals are studied.

Spectral Theory