2008/02/23 by Maxim Derevyagin, Maxim S. Derevyagin, Derevyagin, Maxim S. +3
Mathematics · #30E05 #30E10 #40A15 #41A21 #47A57 (Secondary) #47B36 (Primary) #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical functions and polynomials #Numerical methods for differential equations #Spectral Theory (math.SP) #math.CA #math.CV #math.SP #msc:30E05 #msc:30E10 #msc:40A15 #msc:41A21 #msc:47A57 #msc:47B36
paper · pdf · doi:10.48550/arxiv.0802.3432
18 pages
openalex publication_date 2008/02/23 · arxiv created 2008/06/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.