  The notion of a root functional of a system of polynomials or ideal of
polynomials is a generalization of the notion of a root, in particular, for a
multiple root. A root functional is a linear functional that is defined on a
polynomial ring and annuls the ideal of polynomials. A bounded root functional
is a functional that annuls d-th component of the ideal in some filtration in
this ideal. The paper consider bounded root functionals and their extension
operation for a system of polynomial equation at which the number of equations
is equal to the number of unknows. The extension operation has connection with
the multivariate Bezoutian construction.
