Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 15, pp. 1-30.
Title: The Heun equation and the Calogero-Moser-Sutherland system II:
Perturbation and algebraic solution
Author: Kouichi Takemura (Yokohama City University, Japan)
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.