Bose-Einstein condensation (BEC) is studied for ideal boson gases with a wi
de class of the dispersion relations. A criterion of the BEC. the transitio
n temperature and a fraction of the condensate are calculated under the app
ropriate thermodynamic limits. The correspondence between the dispersion re
lation (spectrum) and the trap potential is shown. This gives the criterion
for the trap shape and the dimensionality of the system.