Derivatives of Faber Polynomials and Markov Inequalities
نویسندگان
چکیده
منابع مشابه
Derivatives of Faber Polynomials and Markov Inequalities
We study asymptotic behavior of the derivatives of Faber polynomials on a set with corners at the boundary. Our results have applications to the questions of sharpness of Markov inequalities for such sets. In particular, the found asymptotics are related to a general Markov-type inequality of Pommerenke and the associated conjecture of Erdős. We also prove a new bound for Faber polynomials on p...
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The rth Faber polynomial of the Laurent series f(t) = t + f0 + f1/t + f2/t + · · · is the unique polynomial Fr(u) of degree r in u such that Fr(f) = tr + negative powers of t. We apply Faber polynomials, which were originally used to study univalent functions, to lattice path enumeration.
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Essentially sharp Markov-type inequalities are known for various classes of polynomials with constraints including constraints of the coefficients of the polynomials. For N and δ > 0 we introduce the class Fn,δ as the collection of all polynomials of the form P x ∑n k h akx k , ak ∈ Z, |ak | ≤ n , |ah| maxh≤k≤n|ak |. In this paper, we prove essentially sharp Markov-type inequalities for polynom...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2002
ISSN: 0021-9045
DOI: 10.1006/jath.2002.3713