On polynomials normalized on an interval
S. I. Kalmykovab
a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok
In this short communication new covering theorems,
two-point distortion theorems and coefficient estimates for
polynomials with a curved majorant on an interval are presented.
Extremal polynomials in these therems are Chebyshev polynomials of
the the second, third and forth kinds. Proofs are based on a new
version of the Schwarz lemma and a univalent condition for
holomorphic functions suggested by Dubinin.
Chebyshev polynomials, Bernstein inequality, conformal
PDF file (432 kB)
S. I. Kalmykov, “On polynomials normalized on an interval”, Dal'nevost. Mat. Zh., 18:2 (2018), 216–266
Citation in format AMSBIB
\paper On polynomials normalized on an interval
\jour Dal'nevost. Mat. Zh.
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