On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane

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 57.3 (2009): 223-229. <http://eudml.org/doc/281272>.

@article{EwaLigocka2009,
abstract = {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 $lim_\{Re z→-∞\}(g(w)-w) = 0$.},
author = {Ewa Ligocka},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {holomorphic functions; univalent functions},
language = {eng},
number = {3},
pages = {223-229},
title = {On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane},
url = {http://eudml.org/doc/281272},
volume = {57},
year = {2009},
}

TY - JOUR
AU - Ewa Ligocka
TI - On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 3
SP - 223
EP - 229
AB - 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 $lim_{Re z→-∞}(g(w)-w) = 0$.
LA - eng
KW - holomorphic functions; univalent functions
UR - http://eudml.org/doc/281272
ER -