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 ∈ ℍ, exp(L(f)(w)) = f(expw). In particular, we prove that the famous class S of univalent functions on the unit disc is homeomorphic via L to the class S(ℍ) of all univalent functions g on ℍ for which g(w+2πi) = g(w) + 2πi and .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-4,
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},
volume = {57},
year = {2009},
pages = {223-229},
zbl = {1189.30028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-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) pp. 223-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-3-4/