Results 71 to 80 of about 2,960 (152)

A new proof of a theorem about generalized orthogonal polynomials

International Journal of Mathematics and Mathematical Sciences, 1991
In this note it is shown that a fairly recent result on the asymptotic distribution of the zeros of generalized polynomials can be deduced from an old theorem of G. Polya, using a minimum of orthogonal polynomial theory.
A. McD. Mercer
doaj   +1 more source

On the Distribution of Zeros and Poles of Rational Approximants on Intervals

Abstract and Applied Analysis, 2012
The distribution of zeros and poles of best rational approximants is well understood for the functions 𝑓(𝑥)=|𝑥|𝛼, 𝛼>0. If 𝑓∈𝐶[−1,1] is not holomorphic on [−1,1], the distribution of the zeros of best rational approximants is governed by the equilibrium ...
V. V. Andrievskii, H.-P. Blatt, R. K. Kovacheva   +2 more
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Real Zeros of Random Polynomials [PDF]

Proceedings of the London Mathematical Society, 1968
Logan, B. F., Shepp, L. A.
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Zeros of Self-Inversive Polynomials [PDF]

Proceedings of the American Mathematical Society, 1953
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Zero distribution of polynomials and polynomial systems

, 2015
The new framework of random polynomials developed by R. Pemantle, I. Rivin and the late O. Schramm has been studied in this thesis. The strong Pemantle-Rivin conjecture asks whether for random polynomials with independent and identically distributed zeros with a common probability distribution μon the complex plane, the empirical measures of their ...
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On critical points of p harmonic functions in the plane

Electronic Journal of Differential Equations, 1994
$ 1 < p < infty $, in the unit disk and equal to a polynomial $ P $ of positive degree on the boundary of this disk, then $ abla u $ has at most deg$P - 1$ zeros in the unit disk.
John L. Lewis
doaj  

Representation formulas for the moments of the density of zeros of orthogonal polynomial sets

Le Matematiche, 1993
The moments of the density of zeros of orthogonal polynomial systems generated by athree-term recurrence relation are represented by Lucas polynomials of the first kind and by Bell polynomials.
Bruna Germano, Paolo Emilio Ricci
doaj  

Zeros of self-inversive polynomials [PDF]

Proceedings of the American Mathematical Society, 1952
Bonsall, F. F., Marden, Morris
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Zero-dimensional families of polynomial systems

Le Matematiche, 2013
If a real world problem is modelled with a system of polynomial equations, the coefficients are in general not exact. The consequence is that small perturbations of the coefficients may lead to big changes of the solutions.
Lorenzo Robbiano, Maria-Laura Torrente
doaj  

p-adic zeros of polynomials

Consider a given system \({\mathcal F}\) of equations \(F_ i(x_ 1,...,x_ n)=0\), \(i=1,2,...,k\), where \(F_ i\) is a polynomial in n variables over a field K such that \(F_ i\) involves only \(m_ i\) monomials with non- zero coefficients; denote \(m_ 1+...+m_ k\) by N. It was shown, for \(K={\mathbb{R}}\), by A. K.
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