English

$a$-potent Schwarz matrices and Bessel-like Jacobi polynomials

Classical Analysis and ODEs 2024-06-18 v1 Spectral Theory

Abstract

We consider the problem of the reconstruction of a Schwarz matrix from exactly one given eigenvalue. This inverse eigenvalue problem leads to the Jacobi orthogonal polynomials~{Pk(n,n)}k=0n1\{P_k^{(-n,n)}\}_{k=0}^{n-1} that can be treated as a discrete finite analogue of Bessel polynomials.

Keywords

Cite

@article{arxiv.2406.11032,
  title  = {$a$-potent Schwarz matrices and Bessel-like Jacobi polynomials},
  author = {Alexander Dyachenko and Carlos M. da Fonseca and Mikhail Tyaglov},
  journal= {arXiv preprint arXiv:2406.11032},
  year   = {2024}
}
R2 v1 2026-06-28T17:07:52.515Z