  The set of trajectories for massive spinless particles on $AdS_{N+1}$
spacetime is described by the dynamical integrals related to the isometry group
SO(2,N). The space of dynamical integrals is mapped one to one to the phase
space of the $N$-dimensional oscillator. Quantizing the system canonically, the
classical expressions for the symmetry generators are deformed in a consistent
way to preserve the $so(2,N)$ commutation relations. This quantization thus
yields new explicit realizations of the spin zero positive energy UIR's of
SO(2,N) for generic $N$. The representations as usual can be characterized by
their minimal energy $\alpha$ and are valid in the whole range of $\alpha$
allowed by unitarity.
