On a Szegö's theorem of orthogonal polynomials

• Autores: Jesús Sánchez-Dehesa Moreno-Cid
• Localización: Revista matemática hispanoamericana, ISSN 0373-0999, Vol. 39, Nº. 6, 1979, pág. 277
• Idioma: inglés
• Títulos paralelos:
  • Teorema de Szegö de polinomios ortogonales
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• Resumen

  • It is found that the asymptotical density of zeros of a system of orthogonal polynomials whose weight function belongs to a wide class of distribution functions has the expression ?(x) = p-1 (1 - x2)-1/2. This result is shown in two completely different ways: (1) from a Szegö theorem and (2) from a Geronimus theorem and a finding recently obtained by the author in a context of Jacobi matrices.