Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type IV. The Relativistic Heun (van Diejen) Case

@article{Ruijsenaars2015HilbertSchmidtOV,
  title={Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type IV. The Relativistic Heun (van Diejen) Case},
  author={Simon N. M. Ruijsenaars},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2015},
  volume={11},
  pages={004}
}
  • S. Ruijsenaars
  • Published 16 April 2014
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
The 'relativistic' Heun equation is an 8-coupling difference equation that gene- ralizes the 4-coupling Heun differential equation. It can be viewed as the time-independent Schrodinger equation for an analytic difference operator introduced by van Diejen. We study Hilbert space features of this operator and its 'modular partner', based on an in-depth analysis of the eigenvectors of a Hilbert{Schmidt integral operator whose integral kernel has a previously known relation to the two difference… 
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