  We examine the occurrence of Bose-Einstein condensation in both
nonrelativistic and relativistic systems with no self-interactions in a general
setting. A simple condition for the occurrence of Bose-Einstein condensation
can be given if we adopt generalized $\zeta$-functions to define the quantum
theory. We show that the crucial feature governing Bose-Einstein condensation
is the dimension $q$ associated with the continuous part of the eigenvalue
spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of
the Klein-Gordon operator for relativistic systems. In either case
Bose-Einstein condensation can only occur if $q\ge3$.
