On polynomials whose zeros are in the unit disk

Some Families of Graphs whose Domination Polynomials are Unimodal

Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=sum_{i=gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $gamma(G)$ is the domination number of $G$. In this paper we present some families of graphs whose domination polynomials are unimodal.

Bounded Approximation by Polynomials Whose Zeros Lie on a Circleo

Asymptotics of polynomials orthogonal over the unit disk with respect to a polynomial weight without zeros on the unit circle

We establish asymptotic formulas for polynomials that are orthogonal over the unit disk with respect to a weight of the form |w(z)|2, where w(z) is a polynomial without zeros on the unit circle |z| = 1. The formulas put in evidence a strong connection between the behavior of the polynomials and the reproducing kernel of an associated weighted Bergman space, which produces interesting new featur...

Orthogonal polynomials on the unit circle: distribution of zeros

Marcellan, F. and E. Godoy, Orthogonal polynomials on the unit circle: distribution of zeros, Journal of Computational and Applied Mathematics 37 (1991) 195-208. In this paper we summarize some results concerning zeros of orthogonal polynomials with respect to an indefinite inner product. We analyze the inverse problem, i.e., a discrete representation for the functional in terms of the n th ort...

An Inequality for Derivatives of Polynomials Whose Zeros Are in a Half-plane

Let Q be a real polynomial of degree N all of whose zeros lie in the half-plane Re z < 0. Let M(r, Q) be the maximum of | Q(z) | on \z\= r and n(r,0) the counting function of the zeros of Q. It is shown that the inequality M(r, Q') « (2r)"'{A' + n(r,0)}M(r, Q) holds for r > 0. It is also shown that Bernstein's inequality characterizes polynomials.