An operator approach to multipoint Pade approximations

Details An operator approach to multipoint Pade approximations An operator approach to multipoint Pade approximations

2008-02-23

arxiv.org/abs/0802.3432v2

Mathematics

Classical Analysis and ODEs

18 pages

Scientific paper

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 Pad\'e approximants to Nevanlinna functions is proved.

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