Polya's theorem for non-entire functions
Polynômes à coefficients unimodulaires sur le cercle unité
Polynômes quadratiques et attracteur de Hénon
Polynomial Growth along Jordan Arcs.
Polynomials of Maximal Index.
Rate of growth of polynomials not vanishing inside a circle.
Remarks on inverse of matrix polynomials
Analysis of a non-classically damped engineering structure, which is subjected to an external excitation, leads to the solution of a system of second order ordinary differential equations. Although there exists a large variety of powerful numerical methods to accomplish this task, in some cases it is convenient to formulate the explicit inversion of the respective quadratic fundamental system. The presented contribution uses and extends concepts in matrix polynomial theory and proposes an implementation...
Remarks on some recent results about polynomials with restricted zeros
We point out certain flaws in two papers published in Ann. Univ. Mariae Curie-Skłodowska Sect. A, one in 2009 and the other in 2011. We discuss in detail the validity of the results in the two papers in question
Reverse Markov inequality.
Schur's Theorem on the Stability of Networks
A complex polynomial is called a Hurwitz polynomial if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in stability checks of electrical networks.In this article we prove Schur's criterion [17] that allows to decide whether a polynomial p(x) is Hurwitz without explicitly computing its roots: Schur's recursive algorithm successively constructs polynomials pi(x) of lesser degree by division with x - c, ℜ {c} < 0, such that pi(x) is Hurwitz if...
Simple polynomials
Smale's Conjecture on Mean Values of Polynomials and Electrostatics
2000 Mathematics Subject Classification: Primary 30C10, 30C15, 31B35.A challenging conjecture of Stephen Smale on geometry of polynomials is under discussion. We consider an interpretation which turns out to be an interesting problem on equilibrium of an electrostatic field that obeys the law of the logarithmic potential. This interplay allows us to study the quantities that appear in Smale’s conjecture for polynomials whose zeros belong to certain specific regions. A conjecture concerning the electrostatic equilibrium...
Small values of polynomials: Cartan, Pólya and others.
Some Characterizations of L-regular Points.
Some estimates of the integral .
Some Estimates of the Integral
Some results concerning the zeros and coefficients of polynomials
Some topological and geometric properties of pseudozero set.
Starlikeness of polynomials and finite Blaschke products
The radius of starlikeness for polynomial mappings and finite Blaschke products with zeroes distributed at equal angles around a circle centered at the origin, as well as with zeroes concentrated at a single point, are considered, and sharp bounds are obtained. Results expressing the radius of starlikeness of an arbitrary polynomial or Blaschke product in terms of the magnitudes of the zeroes are also given. These are also sharp.
Sur la répartition des zéros d'une classe de polynômes.