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arXiv · 2104.01216

Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices

Alexander Dyachenko·Mikhail Tyaglov
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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.

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Alexander Dyachenko, Mikhail Tyaglov. 2021-04-02. Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices. https://arxiv.org/abs/2104.01216

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