On Some Correspondence between Holomorphic Functions in the Unit
Disc and Holomorphic Functions in the Left Halfplane
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 3, pp. 223-229
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We study a correspondence $L$ between some classes of
functions holomorphic in the unit disc and functions holomorphic in the
left halfplane. This correspondence is such that for every $f$ and
$w\in\mathbb H$, $\exp(L(f)(w))=f(\exp w)$.In particular, we prove that the famous class $S$ of univalent functions on
the unit disc is homeomorphic via $L$ to the class $S({\mathbb H})$ of
all univalent functions $g$ on $\mathbb H$ for which $g(w+2\pi i)=g(w)+2\pi i$
and $\lim_{\mathop{\rm Re} z\to-\infty}(g(w)-w)=0$.
Keywords:
study correspondence between classes functions holomorphic unit disc functions holomorphic halfplane correspondence every mathbb exp exp particular prove famous class univalent functions unit disc homeomorphic via class mathbb univalent functions mathbb which lim mathop to infty w
Affiliations des auteurs :
Ewa Ligocka 1
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author = {Ewa Ligocka},
title = {On {Some} {Correspondence} between {Holomorphic} {Functions} in the {Unit} {
Disc} and {Holomorphic} {Functions} in the {Left} {Halfplane}},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {223--229},
year = {2009},
volume = {57},
number = {3},
doi = {10.4064/ba57-3-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba57-3-4/}
}
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%0 Journal Article %A Ewa Ligocka %T On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2009 %P 223-229 %V 57 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4064/ba57-3-4/ %R 10.4064/ba57-3-4 %G en %F 10_4064_ba57_3_4
Ewa Ligocka. On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) no. 3, pp. 223-229. doi: 10.4064/ba57-3-4
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