The order of a linearly invariant family in Cn

Martin Chuaqui, Rodrigo Hernández

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)372-379
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume398
Issue number1
DOIs
StatePublished - 1 Feb 2013

Keywords

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

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