Convolutions of harmonic convex mappings

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dc.creatorDorff, Michael
dc.creatorNowak, Maria
dc.creatorWoloszkiewicz, Magdalena
dc.date2009-03-09
dc.date.accessioned2026-07-07T12:50:32Z
dc.date.available2026-07-07T12:50:32Z
dc.descriptionThe first author proved that the harmonic convolution of a normalized right half-plane mapping with either another normalized right half-plane mapping or a normalized vertical strip mapping is convex in the direction of the real axis. provided that it is locally univalent. In this paper, we prove that in general the assumption of local univalency cannot be omitted. However, we are able to show that in some cases these harmonic convolutions are locally univalent. Using this we obtain interesting examples of univalent harmonic maps one of which is a map onto the plane with two parallel slits.
dc.description15 pages, 4 figure files
dc.identifierhttps://arxiv.org/abs/0903.1595
dc.identifierhttp://arxiv.org/abs/0903.1595
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222713
dc.subjectComplex Variables
dc.subject30C45
dc.titleConvolutions of harmonic convex mappings
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