On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space

Abstract

ABSTRACT. The representation of Nevanlinna Pick Problem is well known, see [71, [8] and [111.The aim of this paper is to find the necessary and sufficient condition for the solution of Nevanlinna lick Problem and to show that there is a one-to-one correspondence between the solutions of the Nevanlinna Pick Problem and the minimal selfadjoint extensions of symmetric linear relation in Hilbert space. Finally, we define the resolvent matrix which gives the solutions of the Nevanlinna Pick Problem.