On the convolution of convex 2-gons

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dc.contributor.authorChuaqui, Martin
dc.contributor.authorHernandez, Rodrigo
dc.contributor.authorLlinares, Adrian
dc.contributor.authorMas, Alejandro
dc.date.accessioned2025-01-20T16:17:59Z
dc.date.available2025-01-20T16:17:59Z
dc.date.issued2024
dc.description.abstractWe study the convolution of functions of the form f alpha ( z) := /I 1+ z \ alpha - 1 1 -z , 2 alpha which map the open unit disk of the complex plane onto polygons of 2 edges when alpha is an element of (0 , 1). Inspired by a work of Cima, we study the limits of convolutions of finitely many f alpha and the convolution of arbitrary unbounded convex mappings. The analysis for the latter is based on the notion of angle at infinity , which provides an estimate for the growth at infinity and determines whether the convolution is bounded or not. A generalization to an arbitrary number of factors shows that the convolution of n randomly chosen unbounded convex mappings has a probability of 1 /n! of remaining unbounded. We provide the precise asymptotic behavior of the coefficients of the functions f alpha . (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
dc.fuente.origenWOS
dc.identifier.doi10.1016/j.jmaa.2024.128387
dc.identifier.eissn1096-0813
dc.identifier.issn0022-247X
dc.identifier.urihttps://doi.org/10.1016/j.jmaa.2024.128387
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/90625
dc.identifier.wosidWOS:001230589700001
dc.issue.numero2
dc.language.isoen
dc.revistaJournal of mathematical analysis and applications
dc.rightsacceso restringido
dc.subjectConvolution
dc.subjectConvex mappings
dc.subject2-gons
dc.titleOn the convolution of convex 2-gons
dc.typeartículo
dc.volumen538
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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