On affine frames with transcendental dilations

Research output: Contribution to journalArticlepeer-review


We answer a question of O. Christensen about affine systems in L 2(ℝ). Specifically, we show that if the dilation factor a > 1 is transcendental, then cancellations cannot occur between different scales, in the conditions for the affine system to form a frame. Such cancellations are known to occur when a is an integer.

Original languageEnglish (US)
Pages (from-to)211-216
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - Jan 2007


  • Affine system
  • Frame
  • Transcendental

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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