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Orthogonal Exponentials for Bernoulli Iterated Function Systems

  • Palle E. T. Jorgensen
  • Keri Kornelson
  • Karen Shuman
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We investigate certain spectral properties of the Bernoulli convolution measures on attractor sets arising from iterated function systems (IFSs) on ℝ. In particular, we examine collections of orthogonal exponential functions in the Hilbert space of square-integrable functions on the attractor. We carefully examine a test case λ = 3/4 in which the IFS has overlap. We also determine rational λ = a/b for which infinite sets of orthogonal exponentials exist.

Keywords

Hilbert Space Nonzero Element Invariance Property Iterate Function System Pisot Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Palle E. T. Jorgensen
    • 1
  • Keri Kornelson
    • 2
  • Karen Shuman
    • 2
  1. 1.Department of MathematicsUniversity of IowaIowa City
  2. 2.Department of Mathematics & StatisticsGrinnell CollegeGrinnell

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