A relationship between a Hankel matrix of Markov parameters and the associated matrix polynomial with some applications
A Reliable Argument Principle Algorithm to Find the Number of Zeros of an Analytic Function in a Bounded Domain.
A simple proof of the Fundamental Theorem of Algebra
In the paper an elementary and simple proof of the Fundamental Theorem of Algebra is given.
A Unified Approach to Methods for the Simultaneous Computation of All Zeros of Generalized Polynomials.
Admissible functions for the Dirichlet space
Zero sets and uniqueness sets of the classical Dirichlet space are not completely characterized yet. We define the concept of admissible functions for the Dirichlet space and then apply them to obtain a new class of zero sets for . Then we discuss the relation between the zero sets of and those of .
Algoritmy na výpočet kořenů polynomu
An Algorithm for the Zeros of Transcendental Functions.
Analytic functions over valued fields.
Annular bounds for polynomial zeros and Schur stability of difference equations.
Applications of stability criteria to time delay systems.
Area Nevanlinna type classes of analytic functions in the unit disk and related spaces
The survey collects many recent advances on area Nevanlinna type classes and related spaces of analytic functions in the unit disk concerning zero sets and factorization representations of these classes and discusses approaches, used in proofs of these results.
Arithmetic implications of the distribution of integral zeros of exponential polynomials
Asymptotic distribution and symmetric means of algebraic numbers
Schur introduced the problem on the smallest limit point for the arithmetic means of totally positive conjugate algebraic integers. This area was developed further by Siegel, Smyth and others. We consider several generalizations of the problem that include questions on the smallest limit points of symmetric means. The key tool used in the study is the asymptotic distribution of algebraic numbers understood via the weak* limits of their counting measures. We establish interesting properties of the...
Asymptotics for the zeros of the generalized Bessel polynomials.
Bernstein classes
One of the classical Bernstein inequalities compares the maxima of a polynomial of a given degree on the interval [-1,1] and on the ellipse in the complex plane with the focuses -1, 1 and the semiaxes . We prove a similar inequality for a branch of an algebraic function of a given degree on the maximal disk of its regularity, with the explicitly given constant, depending on the degree only. In particular, this improves a recent inequality of Fefferman and Narasimhan and answers one of their questions....
Beta-numbers whose conjugates lie near the unit circle
Blaschke-Folgen und Carleson-Mengen.
Bounds of the roots of the real polynomial
An algorithm for the calculation of a lower bound of the absolute values of the roots of a real algebraic polynomial, of an arbitrary degree, is derived. An example is given to compare the bounds calculated by the method proposed and by other methods.
Braiding of the attractor and the failure of iterative algorithms.
Characterization of the Set of Limit Points of the Zeros of Annular Functions.