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 step-by-step process of solving the Nevanlinna-Pick problems for Nevanlinna functions. The process in question leads to three-term 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.