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Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices
Alexander Dyachenko, Mikhail Tyaglov
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…
On generalization of classical Hurwitz stability criteria for matrix polynomials
Xuzhou Zhan, Alexander Dyachenko
In this paper, we associate a class of Hurwitz matrix polynomials with Stieltjes positive definite matrix sequences. This connection leads to an extension of two classical criteria…
Discrete multiple orthogonal polynomials on shifted lattices
Alexander Dyachenko, Vladimir Lysov
We introduce a new class of polynomials of multiple orthogonality with respect to the product of classical discrete weights on integer lattices with noninteger shifts. We give…
Rigidity of the Hamburger and Stieltjes moment sequences
Alexander Dyachenko
This paper aims at finding conditions on a Hamburger or Stieltjes moment sequence, under which the change of at most a finite number of its entries produces another sequence of the…