A geometric interpretation and explicit form for higher-order Hankel operators

TL;DR

This paper provides an explicit differential operator form for higher-order Hankel operators and introduces a Lie-theoretic perspective to analyze their properties, advancing the theoretical understanding of these operators.

Contribution

It presents a new explicit form for higher-order Hankel operators as linear differential operators and introduces a novel Lie-theoretic framework for their study.

Findings

Explicit differential operator form derived for higher-order Hankel operators.

Introduction of a Lie-theoretic perspective for analyzing these operators.

Enhanced theoretical understanding of higher-order Hankel operators.

Abstract

This paper deals with well-known higher-order generalizations of Hankel operators. We show that higher-order Hankel operators can be written explicitly as linear differential operators, and give the exact form of these differential operators. We also intoduce a novel Lie-theoretic perspective from which to study higher-order Hankel operators.