  In 1979 I. Cior\u{a}nescu and L. Zsid\'o have proved a minimum modulus
theorem for entire functions dominated by the restriction to the positive half
axis of a canonical product of genus zero, having all roots on the positive
imaginary axis and satisfying a certain condition.
  Here we prove that the above result is optimal: if a canonical product
{\omega} of genus zero, having all roots on the positive imaginary axis, does
not satisfy the condition in the 1979 paper, then always there exists an entire
function dominated by the restriction to the positive half axis of {\omega},
which does not satisfy the desired minimum modulus conclusion. This has
relevant implication concerning the subjectivity of ultra differential
operators with constant coefficients.
