  The widely accepted assumption that the decay of a resonance proceeds
independently of its production, quantitatively expressed as a factorizing
formula for the differential cross section in the invariant mass of unpolarized
resonance debris, is put under scrutiny. It is shown that the factorization is
always valid for scalar and pseudoscalar resonances, although the usual version
of the formula is not entirely correct. For resonances with nonzero spins the
factorization does not generally take place. We deal in more detail with the
spin-one case, where we show a condition on the decay matrix element that
ensures the validity of the same factorizing formula as in the spinless case.
This condition is satisfied for rho --> pi pi but not, e.g., for K* --> pi K or
a1 --> pi rho. The formalism is applied also to the case when the resonance is
produced not in two-body collisions but in the decay of a heavier particle or
resonance (chain decay). Application of our formulas to the e+e- production in
one-photon approximation agrees with what is known from quantum electrodynamics
and thus provides another test of their soundness.
