Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices
Classical Analysis and ODEs
2021-07-12 v2
Abstract
A method of generating differential operators is used to solve the spectral problem for a generalisation of the Sylvester-Kac matrix. As a by-product, we find a linear differential operator with polynomial coefficients of the first order that has a finite sequence of polynomial eigenfunctions generalising the operator considered by M. Kac. In addition, we explain spectral properties of two related tridiagonal matrices whose shape differ from our generalisation.
Cite
@article{arxiv.2104.01216,
title = {Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices},
author = {Alexander Dyachenko and Mikhail Tyaglov},
journal= {arXiv preprint arXiv:2104.01216},
year = {2021}
}
Comments
10 pages