An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators

Fuente: arXiv
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Main Authors: Alexandersson, Per, Brändén, Petter, Shapiro, Boris
Format: Preprint
Published: 2024
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author Alexandersson, Per
Brändén, Petter
Shapiro, Boris
author_facet Alexandersson, Per
Brändén, Petter
Shapiro, Boris
contents Given a linear ordinary differential operator T with polynomial coefficients, we study the class of closed subsets of the complex plane such that T sends any polynomial (resp. any polynomial of degree exceeding a given positive integer) with all roots in a given subset to a polynomial with all roots in the same subset or to 0. Below we discuss some general properties of such invariant subsets as well as the problem of existence of the minimal under inclusion invariant subset.
format Preprint
id arxiv_https___arxiv_org_abs_2404_14365
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators
Alexandersson, Per
Brändén, Petter
Shapiro, Boris
Classical Analysis and ODEs
Mathematical Physics
Given a linear ordinary differential operator T with polynomial coefficients, we study the class of closed subsets of the complex plane such that T sends any polynomial (resp. any polynomial of degree exceeding a given positive integer) with all roots in a given subset to a polynomial with all roots in the same subset or to 0. Below we discuss some general properties of such invariant subsets as well as the problem of existence of the minimal under inclusion invariant subset.
title An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators
topic Classical Analysis and ODEs
Mathematical Physics
url https://arxiv.org/abs/2404.14365