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Title: Functionals of higher derivative type
Authors: Goh, S.S. 
Issue Date: Aug-1998
Citation: Goh, S.S. (1998-08). Functionals of higher derivative type. Journal of the London Mathematical Society 58 (1) : 111-126. ScholarBank@NUS Repository.
Abstract: Functionals of higher derivative type are linear combinations of functionals of the form f→f(n)(ζ), where n ≥ 2 and 0 < |ζ| < 1. The paper shows that, if L is a functional of higher derivative type and f is a function in the class S of univalent functions that maximises Re{L} over S, then L(f) ≠ 0. In addition, if the function f is a rational function, then it must be a rotation of the Koebe function k(z) = z(1 - z)-2. These results are applied to establish several cases of the two-functional conjecture for functionals of higher derivative type.
Source Title: Journal of the London Mathematical Society
ISSN: 00246107
Appears in Collections:Staff Publications

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