Український математичний конгрес  2009
Максим Деревягін (Інститут прикладної математики і механіки, Донецьк, Україна) The Jacobi matrices approach to multipoint Pade approximation We consider a modification of the famous stepbystep process of solving the NevanlinnaPick problems for Nevanlinna functions. The process in question leads to threeterm recurrence relations with coefficients depending on the spectral parameter. These relations give rise to a linear pencil with two Jacobi matrices. So, under some conditions, one can represent a Nevanlinna function by means of the resolvent of the underlying linear pencil. Finally, the convergence of multipoint Pade approximants appears as the strong resolvent convergence of finite matrix approximations of the linear pencil.
