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

@inproceedings{Dyachenko2021LinearDO, title={Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices}, author={Alexander Dyachenko and Mikhail Tyaglov}, year={2021} }

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.

## One Citation

A note on tridiagonal matrices with zero main diagonal

- Mathematics
- 2021

We find the spectrum of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal provided that the spectrum of the matrix with the same suband superdiagonals and zero main…

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