Sobolev formal orthogonality on algebraic curves and extensions of Favard theorem

• Héctor Pijeira ^[1] ; Yamilet Quintana ^[2] ; José M. Rodríguez ^[1]
  1. [1] Universidad Carlos III de Madrid

     Universidad Carlos III de Madrid

     Madrid, España

     
  2. [2] Universidad Simón Bolívar
• Localización: Jaen journal on approximation, ISSN 1889-3066, ISSN-e 1989-7251, Vol. 3, Nº. 2, 2011, págs. 193-207
• Idioma: inglés
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• Resumen

  • 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.