Geodesic
Integral representations of bounded starlike functions
Annales Polonici Mathematici, Tome 60 (1994) no. 3, pp. 289-297.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

For α ≥ 0 let $ℱ_α$ denote the class of functions defined for |z| 1 by integrating $1/(1-xz)^α$ if α > 0, and log(1/(1-xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf'(z)/f(z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to $ℱ_0$. In general, it is only known that bounded starlike functions belong to $ℱ_α$ for α > 0.
DOI : 10.4064/ap-60-3-289-297
Keywords: Cauchy-Stieltjes integrals, starlike functions

Frode Rønning 1

1 
@article{10_4064_ap_60_3_289_297,
     author = {Frode R{\o}nning},
     title = {Integral representations of bounded starlike functions},
     journal = {Annales Polonici Mathematici},
     pages = {289--297},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {1994},
     doi = {10.4064/ap-60-3-289-297},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap-60-3-289-297/}
}
TY  - JOUR
AU  - Frode Rønning
TI  - Integral representations of bounded starlike functions
JO  - Annales Polonici Mathematici
PY  - 1994
SP  - 289
EP  - 297
VL  - 60
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap-60-3-289-297/
DO  - 10.4064/ap-60-3-289-297
LA  - en
ID  - 10_4064_ap_60_3_289_297
ER  - 
%0 Journal Article
%A Frode Rønning
%T Integral representations of bounded starlike functions
%J Annales Polonici Mathematici
%D 1994
%P 289-297
%V 60
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ap-60-3-289-297/
%R 10.4064/ap-60-3-289-297
%G en
%F 10_4064_ap_60_3_289_297
Frode Rønning. Integral representations of bounded starlike functions. Annales Polonici Mathematici, Tome 60 (1994) no. 3, pp. 289-297. doi : 10.4064/ap-60-3-289-297. http://geodesic.mathdoc.fr/articles/10.4064/ap-60-3-289-297/

Cité par Sources :