# 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} }

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…

## 17 Citations

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We study classes of self-adjoint Hilbert–Schmidt operators, focusing on sufficient conditions for the operators to be positive. The integral kernels for which the conditions hold true encompass…

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