Electron. J. Diff. Eqns., Vol. 2004(2004), No. 15, pp. 1-30.

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

Kouichi Takemura

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.

Submitted May 15, 2003. Published February 5, 2004.
Math Subject Classifications: 33E15, 81Q10.
Key Words: Heun equation, Calogero-Moser-Sutherland system, Inozemtsev model, perturbation, Kato-Rellich theory, trigonometric limit, Heun function, algebraic solution.

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Kouichi Takemura
Department of Mathematical Sciences
Yokohama City University
22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan
email: takemura@yokohama-cu.ac.jp

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