The Ruijsenaars spectral transform, a many-variable Fourier generalization, is claimed to have an inversion formula for complex parameters and to be unitary in four parameter regimes.
Complex hypergeometric functions and integrable many-body problems
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abstract
General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. The derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable $N$-body systems emerging from particular degenerations of the elliptic Ruijsenaars and van Diejen models.
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Ruijsenaars spectral transform
The Ruijsenaars spectral transform, a many-variable Fourier generalization, is claimed to have an inversion formula for complex parameters and to be unitary in four parameter regimes.