Boundary interpolation problem in the classes of generalized Nevanlinna matrix - functions.
by
Arthur Amirshadyan
Donetsk National University, Donetsk, UKRAINE

The paper deals with the boundary indefinite interpolation problem in the classes of generalized Nevanlinna matrix-functions. Given are: real points z_j, symmetric matrices W_j, D_j (j=1, .., m). Find: matrix function F(z) in N_\kappa(Cⁿ) with the properties:

lim_{z [( /\ ) || ( --> )] zj} F(z)=W_j (j=1, .., m); lim_{z [( /\ ) || ( --> )] zj} F'(z) <= D_j (j=1, .., p); lim_{z [( /\ ) || ( --> )] zj} F'(z) >= D_j (j=p+1, .., m).

A one-to-one correspondence between the set of all solutions of the interpolation problem and the set of the so-called G-regular selfadjoint extensions of a model symmetric operator associated with the problem is established. Sufficient conditions for G-regularity of selfadjoint extensions are given in terms of the Weyl function. A formula for the description of all the solutions of the problem is found.

Key words: symmetric operator, generalized rezolvent, Weyl function, boundary interpolation, Pick matrix, Nevanlinna pair.

Date received: June 1, 2002