Explicit Faber Polynomials on Circular Sectors
نویسندگان
چکیده
منابع مشابه
The Faber Polynomials for Circular Sectors
The Faber polynomials for a region of the complex plane, which are of interest as a basis for polynomial approximation of analytic functions, are determined by a conformai mapping of the complement of that region to the complement of the unit disc. We derive this conformai mapping for a circular sector {;: \z\ < 1, |argz| < i/a}, where a > 1, and obtain a recurrence relation for the coefficient...
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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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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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Denoting the real numbers and the nonnegative integers, respectively, by R and N, let S be a subset of Nn for n = 1, 2, . . ., and f be a mapping from Rn into R. We call f a packing function on S if the restriction f |S is a bijection onto N. For all positive integers r1, . . . , rn−1, we consider the integer sector I(r1, . . . , rn−1) = {(x1, . . . , xn) ∈ Nn | xi+1 6 rixi for i = 1, . . . , n...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1992
ISSN: 0025-5718
DOI: 10.2307/2153031