Resumen de Sobolev formal orthogonality on algebraic curves and extensions of Favard theorem

Héctor Esteban Pijeira Cabrera , Yamilet Quintana, José Manuel Rodríguez García

• In this paper Sobolev formal orthogonality on harmonic algebraic curves (Im (h(z)) = 0, h(z) ∈ C[z]) and equipotential curves (|h(z)| = 1, h(z) ∈ C[z]) is defined and studied. In each case, such study is done through the characterization of bilinear forms whose associated functional annihilates at the multiples of (h(z) − h(z))2n+1 for harmonic algebraic curves, or the characterization of bilinear forms whose associated functional annihilates at the multiples of (h(z)h(z)−1)2n+1 for equipotential curves, n ∈ N. Such characterizations allow to find new extensions of Favard theorem in this setting.