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In the previous paper we showed that the wave functions of the quantumRuijsenaars hyperbolic system diagonalize Baxter Q-operators. Using thisproperty and duality relation we prove orthogonality and completeness relationsfor the wave functions or, equivalently, unitarity of the correspondingintegral transform.

Baxter operators in Ruijsenaars hyperbolic system III. Orthogonality and completeness of wave functions