# Nearly invariant subspaces of de Branges spaces

## TL;DR

This paper characterizes nearly invariant subspaces of de Branges spaces without common zeros, showing they are exactly exponential functions times a de Branges space, advancing understanding of their structure.

## Contribution

It provides a precise description of nearly invariant subspaces in de Branges spaces, identifying their form as exponential functions times the original space.

## Key findings

- Nearly invariant subspaces with no common zeros are exponential times de Branges spaces.
- The structure of these subspaces is fully characterized.
- This advances the theoretical understanding of de Branges space substructures.

## Abstract

We prove that the nearly invariant subspaces of a de Branges space which have no common zeros are precisely of the form an exponential function times a de Branges space.