Skip Navigation

Journal of the London Mathematical Society 1998 58(1):111-126; doi:10.1112/S002461079800636X
© 1998 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Goh, S. S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

Functionals of Higher Derivative Type

Say Song Goh

Department of Mathematics, National University of Singapore 10 Kent Ridge Crescent, Singapore 119260. E-mail: matgohss{at}leonis.nus.edu.sg

Received 20 February 1996.

Functionals of higher derivative type are linear combinations of functionals of the form f->f(n)({zeta}), where n≥2 and 0<|{zeta}|<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.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.