Abstract. This paper is devoted to the problems of recapturing a Pick function from its radial boundary values and (estimates of) radial derivatives at points of a finite subset of ${\msbm R}$ and from (estimates of) its radial residues at points of another finite subset of ${\msbm R}$. Necessary and sufficient conditions for solvability of these problems are established, in terms of nonnegativity and rank of the Pick matrix.

AMS Subject Classification (1991): 30E05, 46E22

Received April 2, 1997 and in revised form June 18, 1997. (Registered under 2647/2009.)