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

TL;DR

This paper establishes a correspondence between solutions of the Nehari-Takagi problem and Takagi-Sarason interpolation, introducing generalized gamma-generating matrices to analyze the resolvent matrix.

Contribution

It introduces and studies generalized gamma-generating matrices, linking the Nehari-Takagi problem to Takagi-Sarason interpolation.

Findings

One-to-one correspondence between solutions of the two problems

Introduction of generalized gamma-generating matrices

Characterization of the resolvent matrix within this class

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.