Root Asymptotics of Spectral Polynomials for the Lamé Operator

@article{Borcea2007RootAO,
  title={Root Asymptotics of Spectral Polynomials for the Lam{\'e} Operator},
  author={J. Borcea and B. Shapiro},
  journal={Communications in Mathematical Physics},
  year={2007},
  volume={282},
  pages={323-337}
}
The study of polynomial solutions to the classical Lamé equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schrödinger equation with finite gap potential given by the Weierstrass $$\wp$$-function on the real line. In this paper we establish several… Expand

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