The order of a linearly invariant family in Cn

Martin Chuaqui; Rodrigo Hernández

doi:10.1016/j.jmaa.2012.08.049

The order of a linearly invariant family in Cn

Martin Chuaqui, Rodrigo Hernández

Faculty of Engineering and Science

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

1 Scopus citations

Abstract

We study the (trace) order of the linearly invariant family in the ball Bn defined by {norm of matrix}SF{norm of matrix}≤α, where F:Bn→Cn is locally biholomorphic and SF is the Schwarzian operator. By adapting Pommerenke's approach, we establish a characteristic equation for the extremal mapping that yields an upper bound for the order of the family in terms of α and the dimension n. Lower bounds for the order are established in similar terms by means of examples.

Original language	English
Pages (from-to)	372-379
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	398
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2012.08.049
State	Published - 1 Feb 2013

Keywords

Bergman metric
Extremal mapping
Linearly invariant family
Schwarzian operator
Trace order
Variational method

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10.1016/j.jmaa.2012.08.049

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AB - We study the (trace) order of the linearly invariant family in the ball Bn defined by {norm of matrix}SF{norm of matrix}≤α, where F:Bn→Cn is locally biholomorphic and SF is the Schwarzian operator. By adapting Pommerenke's approach, we establish a characteristic equation for the extremal mapping that yields an upper bound for the order of the family in terms of α and the dimension n. Lower bounds for the order are established in similar terms by means of examples.

KW - Bergman metric

KW - Extremal mapping

KW - Linearly invariant family

KW - Schwarzian operator

KW - Trace order

KW - Variational method

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EP - 379

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

The order of a linearly invariant family in Cn

Abstract

Keywords

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