A Cantor regular set which does not have Markov's property
A characterization of monomial functions.
A family of univalent polynomials in an angular domain.
A generalization of a polynomial lemma of Leja
A generalization of an inequality of Zygmund.
A generalization of Lucas' theorem to vector spaces.
A generalization of the Gauss-Lucas theorem
Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.
A new inequality for a polynomial.
A note on Rouché's theorem
A polynomial with 2k critical values at infinity
We construct a polynomial f:ℂ² → ℂ of degree 4k+2 with no critical points in ℂ² and with 2k critical values at infinity.
A proof of Ilieff's conjecture for polynomials with four zeros.
A remark on the paper of I. Raitchinov "Sur un théorème de Pólya".
A Test for 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 (analog or digital) networks. In this article we prove that a polynomial p can be shown to be Hurwitz by checking whether the rational function e(p)/o(p) can be realized as a reactance of one port, that is as an electrical impedance or admittance consisting of inductors and capacitors. Here e(p) and o(p) denote...
An Asymptotic Formula for the Derivatives of Orthogonal Polynomials of the Unit Circle.
An extremal problem for polynomials with a prescribed value at a given point of the real axis.
Another refinement of Bernstein's inequality.
Asymptotic behavior for the best lower bound of Jensen's functional