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  • An Extremal Problem for Odd Univalent Polynomials 
    Dmitrishin, Dmitriy; Gray, Daniel; Stokolos, Alexander; Tarasenko, Iryna; Дмитришин, Дмитро Володимирович; Тарасенко, Ірина (Springer Science and Business Media Deutschland GmbH, 2023)
    For the univalent polynomials F(z)=∑j=1Najz2j-1 with real coefficients and normalization a1= 1 we solve the extremal problem minaj:a1=1(-iF(i))=minaj:a1=1∑j=1N(-1)j+1aj. We show that the solution is 12sec2(π2N+2), and the ...
  • Sharp Weak Type Estimates for a Family of Soria Bases 
    Dmitrishin, Dmitriy; Дмитришин, Дмитро Володимирович; Hagelstein, Paul; Stokolos, Alex (Springer, 2022)
    Let B be a collection of rectangular parallelepipeds in R3 whose sides are parallel to the coordinate axes and such that B contains parallelepipeds with side lengths of the form s,2Ns,t, where s, t> 0 and N lies in a ...