Nonlinear self-similar measures and their fourier transforms

David Glickenstein, Robert S. Strichartz

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We study measures on ℝn that satisfy a nonlinear self-similar identity involving convolutions. We show that such measures are usually absolutely continuous, and the density has regularity properties that get stronger as the linear terms in the identity get smaller. When there are no linear terms, the density is C∞.

Original languageEnglish (US)
Pages (from-to)205-220
Number of pages16
JournalIndiana University Mathematics Journal
Volume45
Issue number1
DOIs
StatePublished - Jan 1 1996
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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