Classification of linear differential operators with an invariant subspace of monomials

TL;DR

This paper provides a comprehensive classification of linear differential operators that have finite-dimensional invariant subspaces spanned by monomials, advancing understanding of their structure and properties.

Contribution

It offers the first complete classification of such operators, identifying all cases where monomial subspaces are invariant under linear differential operators.

Findings

Identifies all linear differential operators with monomial invariant subspaces.

Characterizes the structure of these operators comprehensively.

Provides a basis for further research in invariant subspace theory.

Abstract

A complete classification of linear differential operators possessing finite-dimensional invariant subspace with a basis of monomials is presented.