Abstract
For a pair of conjugate trigonometrical polynomials C(t)=∑j=1 Najcosjt, S(t)=∑j=1 Najsinjt with real coefficients and normalization a1=1 the following extremal value is found: supa2,…,aNmint{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 |
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Pages (from-to) | 591-596 |
Number of pages | 6 |
Journal | Comptes Rendus Mathematique |
Volume | 357 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2019 |