An inverse problem in Polya-Schur theory. I. Non-genegerate and degenerate operators
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916217714900992 |
|---|---|
| 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 |