  In a Freud-type weighted ($w$) space, introducing another weight ($v$) with
infinitely many roots, we give a complete and minimal system with respect to
$vw$, by deleting infinitely many elements from the original orthonormal system
with respect to $w$. The construction of the conjugate system implies an
interpolation problem at infinitely many nodes. Besides the existence, we give
some convergence properties of the solution.
