Infinite Hankel Block Matrices, Extremal Problems

TL;DR

This paper introduces a novel approach using matrix analogues of eigenvalues to solve extremal problems related to infinite Hankel block matrices, connecting with classical methods when scalar cases are considered.

Contribution

It develops a new framework for extremal problems involving infinite Hankel block matrices using matrix eigenvalue concepts, extending classical scalar approaches.

Findings

Formulation of extremal Nehary problem using matrix eigenvalues

Connection to Adamjan-Arov-Krein approach in scalar case

Potential new methods for analyzing Hankel block matrices

Abstract

In this paper we use the matrix analogue of eigenvalue $\rho_{min}^{2}$ to formulate and to solve the extremal Nehary problem. When $\rho_{min}$ is a scalar, our approach coincides with Adamjan-Arov-Krein approach.