Minimal subsystems of given mean dimension in Bernstein spaces

TL;DR

This paper constructs minimal subsystems with prescribed mean dimension in Bernstein spaces, expanding understanding of dynamical systems in band-limited function spaces.

Contribution

It provides a constructive proof of minimal subsystems with any mean dimension less than twice the bandwidth in Bernstein spaces.

Findings

Existence of minimal subsystems with arbitrary mean dimension below twice the bandwidth.

Extension of results to real-valued function spaces.

Constructive method for identifying such subsystems.

Abstract

In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributions. We give a constructive proof of the existence of minimal subsystems with any given mean dimension strictly less than twice its band-width. A version of real-valued function spaces is considered as well.