On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space. (English) Zbl 0889.47006

El-Sabbagh, A. A.

Int. J. Math. Math. Sci. 20, No. 3, 457-464 (1997).

Summary: The representation of Nevanlinna Pick Problem is well-known. The aim of this paper is to find a necessary and sufficient condition for the solution of the 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 relations in Hilbert space. Finally, we define the resolvent matrix which gives the solutions of the Nevanlinna Pick Problem.

MSC:

47A20	Dilations, extensions, compressions of linear operators
47A57	Linear operator methods in interpolation, moment and extension problems

Keywords:

compressed resolvent; Nevanlinna Pick Problem; minimal selfadjoint extensions of symmetric linear relations; resolvent matrix