Generalized $\gamma$-generating matrices and Nehari-Takagi problem

Abstract

Under certain mild assumption, we establish a one-to-one correspondence between solutions of the Nehari-Takagi problem and solutions of some Takagi-Sarason interpolation problem. The resolvent matrix of the Nehari-Takagi problem is shown to belong to the class of so-called generalized $\gamma$-generating matrices, which is introduced and studied in the paper.