  We consider the problem of finding a $d$-dimensional spectral density through
a moment problem which is characterized by an integer parameter $\nu$. Previous
results showed that there exists an approximate solution under the regularity
condition $\nu\geq d/2+1$. To realize the process corresponding to such a
spectral density, one would take $\nu$ as small as possible. In this letter we
show that this condition can be weaken as $\nu\geq d/2$.
