On weighted compositions preserving the Carathéodory class

Irina Arévalo; Rodrigo Hernández; María J. Martín; Dragan Vukotić

doi:10.1007/s00605-017-1093-3

On weighted compositions preserving the Carathéodory class

Irina Arévalo, Rodrigo Hernández, María J. Martín, Dragan Vukotić

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We characterize in various ways the weighted composition transformations which preserve the class P of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for various special cases of symbols and identify the fixed points of such transformations.

Original language	English
Pages (from-to)	459-477
Number of pages	19
Journal	Monatshefte fur Mathematik
Volume	187
Issue number	3
DOIs	https://doi.org/10.1007/s00605-017-1093-3
State	Published - 1 Nov 2018
Externally published	Yes

Keywords

Angular derivative
Fixed points
Functions with positive real part (Carathéodory class)
Inner functions
Weighted composition transformation

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10.1007/s00605-017-1093-3

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title = "On weighted compositions preserving the Carath{\'e}odory class",

abstract = "We characterize in various ways the weighted composition transformations which preserve the class P of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for various special cases of symbols and identify the fixed points of such transformations.",

keywords = "Angular derivative, Fixed points, Functions with positive real part (Carath{\'e}odory class), Inner functions, Weighted composition transformation",

author = "Irina Ar{\'e}valo and Rodrigo Hern{\'a}ndez and Mart{\'i}n, {Mar{\'i}a J.} and Dragan Vukoti{\'c}",

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AU - Arévalo, Irina

AU - Hernández, Rodrigo

AU - Martín, María J.

AU - Vukotić, Dragan

PY - 2018/11/1

Y1 - 2018/11/1

N2 - We characterize in various ways the weighted composition transformations which preserve the class P of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for various special cases of symbols and identify the fixed points of such transformations.

AB - We characterize in various ways the weighted composition transformations which preserve the class P of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for various special cases of symbols and identify the fixed points of such transformations.

KW - Angular derivative

KW - Fixed points

KW - Functions with positive real part (Carathéodory class)

KW - Inner functions

KW - Weighted composition transformation

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JO - Monatshefte fur Mathematik

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On weighted compositions preserving the Carathéodory class

Abstract

Keywords

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