A Weaker Regularity Condition for the Multidimensional ν-Moment Problem

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 weakened as
$\nu \geq $
d/2.