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.
Baxter operators in Ruijsenaars hyperbolic system III. Orthogonality and completeness of wave functions
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In the previous paper we showed that the wave functions of the quantum Ruijsenaars hyperbolic system diagonalize Baxter Q-operators. Using this property and duality relation we prove orthogonality and completeness relations for the wave functions or, equivalently, unitarity of the corresponding integral transform.
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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.