On density of shift-invariant subspaces of some inductive limit spaces

TL;DR

This paper establishes necessary and sufficient conditions for the density of shift-invariant subspaces within a specific space of integrable functions with bounded support, using the inductive limit topology.

Contribution

It provides a complete characterization of when shift-invariant subspaces are dense in the space of integrable functions with bounded support under the inductive limit topology.

Findings

Characterization of density conditions for shift-invariant subspaces

Application of inductive limit topology to function space analysis

Theoretical framework for understanding subspace density in $\

Abstract

Necessary and sufficient conditions are given for density of shift-invariant subspaces of the space $\mathcal{L}$ of integrable functions of bounded support with the inductive limit topology.