On some correspondence between holomorphic functions in the unit disc and holomorphic functions in the left halfplane

• Autorzy: Ligocka, E.
• 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 ƒ and w ∈ H, exp(L(ƒ)(w)) = ƒ(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(H) of all univalent functions g on H for which = g(w) + 2 πi) = g(w) + 2 πi and limRe z →-- ∞(g(w) - w)=0.

Słowa kluczowe

EN

holomorphic functions; univalent functions; class S; exponential function; logarithm

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2009
• Tom: Vol. 57, no 3-4
• Strony: 223-229
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Ligocka, E.

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

Bibliografia

• [Ch] A. Chéritat, Relatively compact Siegel discs with non-locally connected boundaries, arXiv:0906.1048, 2009.
• [D] P. L. Duren, Univalent Functions, Springer, New York, 1983.
• [K] J. Krzyż, Quasicircles and harmonic measure, Ann. Acad. Sci. Fenn. Ser. AI Math. 12 (1987), 19-24.
• [P] Ch. Pommerenke, Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975.