International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 3, Pages 457-464
doi:10.1155/S0161171297000628

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

A. A. El-Sabbagh

 Department of Mathematics, Faculty of Engineering, Zagazig University, Shoubra, 108 Shoubra Street, Cairo, Egypt
Received 19 June 1995; Revised 1 December 1995

Abstract

The representation of Nevanlinna Pick Problem is well known, see [7], [8] and [11]. The aim of this paper is to find the necessary and sufficient condition for the solution of Nevanlinna Pick 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.