This article examines the asymptotic behavior of the Widom factors, denoted W n, for
Chebyshev polynomials of finite unions of Jordan arcs. We prove that, in contrast to Widom's …

There is no surprise that arithmetic properties of integral ('whole') numbers are controlled by
analytic functions of complex variable. At the same time, the values of analytic functions …

We consider weighted Chebyshev polynomials on the unit circle corresponding to a weight
of the form (z− 1) s where s> 0. For integer values of s this corresponds to prescribing a zero …

This article examines the asymptotic behavior of the Widom factors, denoted $\mathcal {W}
_n $, for Chebyshev polynomials of finite unions of Jordan arcs. We prove that, in contrast to …

We study residual polynomials, R_ x_0, n^(e) R x 0, n (e), e ⊂ R e⊂ R, x_0 ∈ R \ ex 0∈
R\e, which are the degree at most n polynomials with R (x_0)= 1 R (x 0)= 1 that minimize …

We continue our study of the Widom factors for L p (μ) extremal polynomials initiated in
(Alpan and Zinchenko, 2020). In this work we characterize sets for which the lower bounds …

Abstract Let K⊂ C be a compact set in the plane whose logarithmic capacity c (K) is strictly
positive. Let P n (K) be the space of monic polynomials of degree n, all of whose zeros lie in …

We employ the generalized Remez algorithm, initially suggested by PTP Tang, to perform an
experimental study of Chebyshev polynomials in the complex plane. Our focus lies …

We investigate Chebyshev polynomials corresponding to Jacobi weights and determine
monotonicity properties of their related Widom factors. This complements work by Bernstein …

We consider a compact, polynomially convex, regular set $ K\subset\mathbb {C} $ and a
sequence $(p_n) _ {n= 1}^\infty $ of polynomials with uniformly bounded zeros and such that …