Nevanlinna-Pick interpolation with boundary data
Versions of the Nevanlinna-Pick interpolation problems (\textit{C. R. Nevanlinna} [Ann. Acad. Sci. Fennicae (A) 13, No. 1, 1-17 (1916; JFM 47.0271.02)], in which the interpolation nodes are on \(\partial D\), the unit circle, and the interpolation values on the boundary of the allowed region, are studied. The solvability criterion of the problem is found for interpolating functions in the Carathéodory class \(C\) and for functions in the Schur class \(S\). A nonempty problem solution set for \((\partial NPC)\), \((\partial NPC)'\) depends on the Pick matrix (whether it is positive, semidefinite and saturated). Similar relations are valid for \((\partial NPS)\) and \((\partial NPS)'\).
scientific article; zbMATH DE number 1129333
scientific article