A proof of the Veselov Conjecture for segments

TL;DR

This paper proves Veselov's conjecture regarding the zeros of Wronskians formed from consecutive Hermite polynomials, advancing understanding of polynomial zero distributions.

Contribution

It provides a proof of Veselov's conjecture specifically for Wronskians with entries as consecutive Hermite polynomials.

Findings

Zeros of the Wronskians are located as predicted by Veselov's conjecture.

The proof confirms the conjecture for the case of Hermite polynomial entries.

Enhances theoretical understanding of polynomial Wronskian zero distributions.

Abstract

In this note, we prove Veselov's conjecture on the zeros of Wronskians whose entries are Hermite polynomials when the degrees of the polynomials are consecutive positive integres.