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

• Autorzy: Ewa Ligocka
• Języki publikacji: EN

Abstrakty

EN

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 $lim_{Re z→-∞}(g(w)-w) = 0$.

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: 57
• Numer: 3
• Strony: 223-229

Daty

wydano

2009

Twórcy

autor

Ewa Ligocka

• Pasteura 4/6 m. 31, 02-093 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba57-3-4