  By means of a truncation condition on the parameters, the elliptic
Ruijsenaars difference operators are restricted onto a finite lattice of points
encoded by bounded partitions. A corresponding orthogonal basis of joint
eigenfunctions is constructed in terms of polynomials on the joint spectrum. In
the trigonometric limit, this recovers the diagonalization of the truncated
Macdonald difference operators by a finite-dimensional basis of Macdonald
polynomials.
