This article is cited in 3 papers

Holomorphic maps of the disk into itself with invariant diameter and bounded distortion

O. S. Kudryavtseva

Chair of Applied Mathematics and Information Science, Volzhskii Institute of Humanities (Affiliation), Volgograd State University, 11 Sorok Let Pobedy str., Volzhskii, Volgograd oblast, 404133 Russia

Abstract: We consider a problem of embeddability of holomorphic map of the unit disk into itself with invariant diameter and bounded distortion into one-parameter semigroup. Here we require that the elements of one-parameter semigroup have the same properties as the original map does. We obtain embeddability criteria, the solution is given in terms of the Königs function.

Keywords: one-parameter semigroup, fractional iterates, infinitesimal generator, Königs function, fixed points.

UDC: 517.546

Received: 08.01.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2015, 59:8, 41–51

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