On the problem Ax=\lambda Bx in max algebra: every system of intervals is a spectrum

TL;DR

This paper studies the eigenproblem Ax= Bx in max algebra and demonstrates that any finite system of real intervals and points can be realized as its spectrum, revealing the problem's rich spectral structure.

Contribution

It shows that every finite system of real intervals and points can be represented as the spectrum of the max algebra eigenproblem Ax= Bx, expanding understanding of spectral sets in max algebra.

Findings

Any finite system of real intervals and points can be realized as a spectrum.

The spectrum of the eigenproblem in max algebra can be arbitrarily complex.

The result connects spectral theory with interval systems in max algebra.

Abstract

We consider the two-sided eigenproblem Ax=\lambda Bx over max algebra. It is shown that any finite system of real intervals and points can be represented as spectrum of this eigenproblem.