Characterisations of Partition of Unities Generated by Entire Functions in Cd

Ole Christensen, Hong Oh Kim, Rae Young Kim

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Collections of functions forming a partition of unity play an important role in analysis. In this paper we characterise for any N∈N the entire functions P for which the partition of unity condition ∑n∈ZdP(x+n)χ[0,N]d(x+n)=1 holds for all x∈Rd. The general characterisation leads to various easy ways of constructing such entire functions as well. We demonstrate the flexibility of the approach by showing that additional properties like continuity or differentiability of the functions (Pχ[0,N]d)(⋅+n) can be controlled. In particular, this leads to easy ways of constructing entire functions P such that the functions in the partition of unity belong to the Feichtinger algebra.
Original languageEnglish
JournalBulletin of the Australian Mathematical Society
Volume95
Issue number2
Pages (from-to)281-290
Number of pages10
ISSN0004-9727
DOIs
Publication statusPublished - 2017

Keywords

  • Entire functions
  • Feichtinger algebra
  • Partition of unity

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