An operator approach to multipoint Pade approximations

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First, an abstract scheme of constructing biorthogonal rational systems related to some interpolation problems is proposed. We also present a modification of the famous step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question gives rise to three-term recurrence relations with coefficients depending on the spectral parameter. These relations can be rewritten in the matrix form by means of two Jacobi matrices. As a result, a convergence theorem for multipoint Padé approximants to Nevanlinna functions is proved.
18 pages

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Classical Analysis and ODEs, Complex Variables, Spectral Theory, 30E05, 41A21, 47B36 (Primary); 30E10, 40A15, 47A57 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/163716

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0802.3432
 http://arxiv.org/abs/0802.3432

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arXiv