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The Heun equation and the Calogero-Moser-Sutherland system II: Perturbation and algebraic solution

Keywords: Heun equation , Calogero-Moser-Sutherland system , Inozemtsev model , perturbation , Kato-Rellich theory , trigonometric limit , Heun function , algebraic solution.

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Abstract:

We apply a method of perturbation for the $BC_1$ Inozemtsev model from the trigonometric model and show the holomorphy of perturbation. Consequently, the convergence of eigenvalues and eigenfuncions which are expressed as formal power series is proved. We investigate also the relationship between $L^2$ space and some finite dimensional space of elliptic functions.

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