2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60457Let a sequence $(P_n)$ of polynomials in one complex variable satisfy a recurre ce relation with length growing slowlier than linearly. It is shown that $(P_n) $ is an orthonormal basis in $L^2_μ$ for some measure $μ$ on $\C$, if and o ly if the recurrence is a $3-$term relation with special coefficients. The supp rt of $μ$ lies on a straight line. This result is achieved by the analysis of a formally normal irreducible Hessenberg operator with only finitely many nonzero entries in every row. It generalizes the classical Favard's Theorem and the Representation Theorem.5 pagesFunctional Analysis41A10, 47B15text