On a family of extremal polynomials

Dmitriy Dmitrishin, Andrey Smorodin, Alex Stokolos

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

For a pair of conjugate trigonometrical polynomials C(t)=∑j=1 Najcos⁡jt, S(t)=∑j=1 Najsin⁡jt with real coefficients and normalization a1=1 the following extremal value is found: supa2,…,aN⁡mint⁡{C(t):S(t)=0}=−[Formula presented]. An application of this result in geometric complex analysis is shown. Several conjectures for a number of extremal problems on classes of polynomials are suggested.

Original languageEnglish
Pages (from-to)591-596
Number of pages6
JournalComptes Rendus Mathematique
Volume357
Issue number7
DOIs
StatePublished - Jul 2019

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