On the convolution of convex 2-gons

Chuaqui, MartinFacultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile (författare)

We study the convolution of functions of the form [Formula presented] which map the open unit disk of the complex plane onto polygons of 2 edges when α∈(0,1). Inspired by a work of Cima, we study the limits of convolutions of finitely many fα 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 fα.

Hernández, RodrigoFacultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar, Chile (författare)
Llinares, AdriánUmeå universitet,Institutionen för matematik och matematisk statistik,Departamento de Análisis Matemático y Matemática Aplicada, Universidad Complutense de Madrid, Madrid, Spain(Swepub:umu)adll0001 (författare)
Mas, AlejandroDepartamento de Análisis Matemático, Universidad de Valencia, Burjassot, Spain (författare)
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, ChileFacultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar, Chile (creator_code:org_t)

Ingår i:Journal of Mathematical Analysis and Applications: Elsevier538:20022-247X1096-0813

Av författaren/redakt...: Chuaqui, Martin; Hernández, Rodri ...; Llinares, Adrián; Mas, Alejandro

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