  The spinless Salpeter equation is the combination of relativistic kinematics
with some static interaction potential. The nonlocal nature of the Hamiltonian
resulting from this approximation renders difficult to obtain rigorous analytic
statements on resulting solutions. In view of this rather unsatisfactory state
of affairs, we calculate analyic upper bounds on the involved energy levels,
and, for the Coulomb potential, on the ground-state energy at the critical
value of the coupling constant.
