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.