On a family of extremal polynomials

Dmitriy Dmitrishin; Andrey Smorodin; Alex Stokolos

doi:10.1016/j.crma.2019.06.010

On a family of extremal polynomials

Dmitriy Dmitrishin
, Andrey Smorodin
, Alex Stokolos

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

For a pair of conjugate trigonometrical polynomials C(t)=∑_j=1 ^Na_jcos⁡jt, S(t)=∑_j=1 ^Na_jsin⁡jt with real coefficients and normalization a₁=1 the following extremal value is found: supa₂,…,a_N⁡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 language	English
Pages (from-to)	591-596
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	357
Issue number	7
DOIs	https://doi.org/10.1016/j.crma.2019.06.010
State	Published - Jul 2019

Scopus Subject Areas

General Mathematics

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title = "On a family of extremal polynomials",

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.",

author = "Dmitriy Dmitrishin and Andrey Smorodin and Alex Stokolos",

note = "Publisher Copyright: {\textcopyright} 2019 Acad{\'e}mie des sciences",

year = "2019",

month = jul,

doi = "10.1016/j.crma.2019.06.010",

language = "English",

volume = "357",

pages = "591--596",

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T1 - On a family of extremal polynomials

AU - Dmitrishin, Dmitriy

AU - Smorodin, Andrey

AU - Stokolos, Alex

PY - 2019/7

Y1 - 2019/7

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85068473309

U2 - 10.1016/j.crma.2019.06.010

DO - 10.1016/j.crma.2019.06.010

M3 - Article

AN - SCOPUS:85068473309

SN - 1631-073X

VL - 357

SP - 591

EP - 596

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 7

ER -

On a family of extremal polynomials

Abstract

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