41 citations · 121 across the 22 of their papers we have counts for
16 papers · 1 filter
-potent Schwarz matrices and Bessel-like Jacobi polynomials
Alexander Dyachenko, Carlos M. da Fonseca, Mikhail Tyaglov
We consider the problem of the reconstruction of a Schwarz matrix from exactly one given eigenvalue. This inverse eigenvalue problem leads to the Jacobi orthogonal polynomials~$\{P…
A generalized Hermite-Biehler theorem
Rostyslav Kozhan, Mikhail Tyaglov
The classical Hermite-Biehler theorem describes possible zero sets of complex linear combinations of two real polynomials whose zeros strictly interlace. We provide the full charac…
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 the number of non-real zeroes of a homogeneous differential polynomial and a generalization of the Laguerre inequalities
Mikhail Tyaglov, Mohamed J. Atia
Given a real polynomial with only real zeroes, we find upper and lower bounds for the number of non-real zeroes of the differential polynomial $$ F_{\varkappa}[p](z):= p(z)p''(…
Hermite-Poulain theorems for linear finite difference operators
Olga Katkova, Mikhail Tyaglov, Anna Vishnyakova
We establish analogues of the Hermite-Poulain theorem for linear finite difference operators with constant coefficients defined on sets of polynomials with roots on a straight line…
Total nonnegativity of finite Hurwitz matrices and root location of polynomials
Mohammad Adm, Jürgen Garloff, Mikhail Tyaglov
In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the \emph{closed} left half-plane of the complex plane, its finite H…
Self-interlacing polynomials II: Matrices with self-interlacing spectrum
Mikhail Tyaglov
An matrix is said to have a self-interlacing spectrum if its eigenvalues , , are distributed as follows A…
Self-interlacing polynomials
Mikhail Tyaglov
We describe a new subclass of the class of real polynomials with real simple roots called self-interlacing polynomials. This subclass is isomorphic to the class of real Hurwitz sta…
Linear finite difference operators preserving Laguerre-Pólya class
O. Katkova, M. Tyaglov, A. Vishnyakova
We completely describe all finite difference operators of the form preserving the Laguerre-Pólya class of entire functions…
Circulants and critical points of polynomials
Olga Kushel, Mikhail Tyaglov
We prove that for any circulant matrix of size with the monic characteristic polynomial , the spectrum of its submatrix construct…
Szegő's theorem for matrix orthogonal polynomials
Maxim Derevyagin, Olga Holtz, Sergey Khrushchev +1
We extend some classical theorems in the theory of orthogonal polynomials on the unit circle to the matrix case. In particular, we prove a matrix analogue of Szegő's theorem. As a…
Hurwitz rational functions
Yury S. Barkovsky, Mikhail Tyaglov
A generalization of Hurwitz stable polynomials to real rational functions is considered. We establishe an analogue of the Hurwitz stability criterion for rational functions and int…
Generalized Hurwitz polynomials
Mikhail Tyaglov
We describe a wide class of polynomials, which is a natural generalization of Hurwitz stable polynomials. We also give a detailed account of so-called self-interlacing polynomials,…
Maximal univalent disks of real rational functions and Hermite-Biehler polynomials
V. Kostov, B. Shapiro, M. Tyaglov
The well-known Hermite-Biehler theorem claims that a univariate monic polynomial s of degree k has all roots in the open upper half-plane if and only if s=p+iq where p and q are re…
Structured matrices, continued fractions, and root localization of polynomials
Olga Holtz, Mikhail Tyaglov
We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type…
On the number of real critical points of logarithmic derivatives and the Hawaii conjecture
Mikhail Tyaglov
For a given real entire function with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions and .…