Van Vleck spectra of high-order Heun operators:\ finite-band universality and exterior asymptotics

Boris Shapiro

We study high-order analogues of the classical Heun operator of Fuchs index one, \[ \dq=\sum_{i=1}^k Q_i(z)\frac{d^i}{dz^i}, \qquad °Q_i\le i+1, \qquad °Q_k=k+1. \] For a fixed deg…