Fourier-Padé Approximants for Nikishin systems
- Lopez Lagomasino, G. 1
- Minguez Ceniceros, J. 2
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1
Universidad Carlos III de Madrid
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2
Universidad de La Rioja
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ISSN: 0176-4276
Año de publicación: 2008
Volumen: 30
Número: 1
Páginas: 53-69
Tipo: Artículo
beta Ver similares en nube de resultadosOtras publicaciones en: Constructive Approximation
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Resumen
We study type I Fourier-Padé approximation for certain systems of functions formed by the Cauchy transform of finite Borel measures supported on bounded intervals of the real line. This construction is similar to type I Hermite-Padé approximation. Instead of power series expansions of the functions in the system, we take their development in a series of orthogonal polynomials. We give the exact rate of convergence of the corresponding approximants. The answer is expressed in terms of the extremal solution of an associated vector-valued equilibrium problem for the logarithmic potential. © 2008 Springer Science+Business Media, LLC.