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
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References
SHOWING 1-10 OF 39 REFERENCES
Eigenvectors of tridiagonal matrices of Sylvester type
- Mathematics
- 2008
Eigenvectors of the tridiagonal matrices of Sylvester type are explicitly determined. These are closely related to orthogonal polynomials named after Krawtchouk, (dual) Hahn and Racah as well as to…
The interesting spectral interlacing property for a certain tridiagonal matrix
- Mathematics
- 2020
In this paper, a new tridiagonal matrix, whose eigenvalues are the same as the Sylvester-Kac matrix of the same order, is provided. The interest of this matrix relies also in that the spectrum of a…
A new type of Sylvester–Kac matrix and its spectrum
- MathematicsLinear and Multilinear Algebra
- 2019
ABSTRACT The Sylvester–Kac matrix, sometimes known as Clement matrix, has many extensions and applications throughout more than a century of its existence. The computation of the eigenvalues or even…
Random Walk and the Theory of Brownian Motion
- Mathematics
- 1947
(1947). Random Walk and the Theory of Brownian Motion. The American Mathematical Monthly: Vol. 54, No. 7P1, pp. 369-391.
Fibonacci polynomials and Sylvester determinant of tridiagonal matrix
- MathematicsAppl. Math. Comput.
- 2010
A finite quantum oscillator model related to special sets of Racah polynomials
- Mathematics
- 2016
In [R. Oste and J. Van der Jeugt, arXiv: 1507.01821 [math-ph]] we classified all pairs of recurrence relations in which two (dual) Hahn polynomials with different parameters appear. Such pairs are…
Doubling (Dual) Hahn Polynomials: Classification and Applications
- Mathematics
- 2016
We classify all pairs of recurrence relations in which two Hahn or dual Hahn polynomials with different parameters appear. Such couples are referred to as (dual) Hahn doubles. The idea and interest…
Evaluation of Sylvester type determinants using block-triangularization
- Mathematics
- 2005
It is shown that the values of Sylvester type determinants for various orthogonal polynomials considered by Askey in [R.Askey, Evaluation of some determinants, Proceedings of the 4th ISAAC Congress,…