Article contents
FUNCTIONALS OF HIGHER DERIVATIVE TYPE
Published online by Cambridge University Press: 01 August 1998
Abstract
Functionals of higher derivative type are linear combinations of functionals of the form f→f(n)(ζ), where n[ges ]2 and 0<[mid ]ζ[mid ]<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.
- Type
- Notes and Papers
- Information
- Copyright
- The London Mathematical Society 1998
- 1
- Cited by