Varying weights for orthogonal polynomials with monotonically varying recurrence coefficients

• Autores: Alexander IIvanovich Aptekarev, Jeffrey S. Geronimo, Walter Van Assche
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 150, Nº 2, 2008, págs. 214-238
• Idioma: inglés
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• Resumen

  • We consider orthogonal polynomials , where n is the degree of the polynomial and N is a discrete parameter. These polynomials are orthogonal with respect to a varying weight WN which depends on the parameter N and they satisfy a recurrence relation with varying recurrence coefficients which we assume to be varying monotonically as N tends to infinity. We establish the existence of the limit and link this limit to an external field for an equilibrium problem in logarithmic potential theory.