Fractal Spaces

  • Kathy D. Merrill
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


In this chapter we present a fractal space GMRA created by Dutkay and Jorgensen in 2006. These authors enlarged fractals formed by iterated function systems in Euclidean space, in order to allow translation invariance. They then built a multiresolution structure on the resulting L2 space with respect to Hausdorff measure extended to this enlarged set. We describe the Dutkay/Jorgensen construction on the spaces associated with the ordinary Cantor set and with other fractals, the use of generalized filters to build wavelets, and a version of a Fourier transform on this space due to Dutkay.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Kathy D. Merrill
    • 1
  1. 1.Department of MathematicsThe Colorado CollegeColorado SpringsUSA

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