Bezoutians and projections

AbstractWith each polynomial p of degree n whose roots lie inside the unit disc we may associate the n-dimensional space of all solutions of the recurrence relation whose coefficients are those of p (considered as a subspace of 12). The main result consists in establishing a close relation between the Bezoutian of two such polynomials (of the same degree) and the projection operator onto one of the corresponding spaces along the complement of the other. The note forms a loose continuation of the author's investigations of the infinite companion matrix—the generating function of the infinite companion matrix of a polynomial p appears thus as a particular case; the corresponding Bezoutian is that of the pair p and zn