The Carathéodory–Fejér interpolation on the polydisc
Tom 254 / 2020
Studia Mathematica 254 (2020), 265-293 MSC: Primary 47A20, 47A56, 47B35; Secondary 30E05, 30H05, 30H10. DOI: 10.4064/sm190314-18-8 Opublikowany online: 6 April 2020
We give an algorithm for finding a solution to the Carathéodory–Fejér interpolation problem on the polydisc, whenever a solution exists. A necessary condition for the existence of a solution becomes apparent from this algorithm. A generalization of the well-known theorem due to Nehari has been obtained. A proof of the Korányi–Pukánszky theorem also follows from these ideas.