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Number Theoretic Considerations Related to the Scaling of Spectra of Cantor-Type Measures

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Abstract

We investigate some relations between number theory and spectral measures related to the harmonic analysis of a Cantor set. Specifically, we explore ways to determine when an odd natural number m generates a complete or incomplete Fourier basis for a Cantor-type measure with scale g.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, 4393, Orlando, FL, 32816-1364, USA

    D. E. Dutkay & I. Kraus

Authors
  1. D. E. Dutkay
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  2. I. Kraus
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Correspondence to D. E. Dutkay.

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Dedicated to the memory of Jean-Pierre Kahane

This material is based upon work supported by the National Science Foundation under Award No. 1356233. This work was partially supported by a grant from the Simons Foundation (#228539 to Dorin Dutkay).

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Dutkay, D.E., Kraus, I. Number Theoretic Considerations Related to the Scaling of Spectra of Cantor-Type Measures. Anal Math 44, 335–367 (2018). https://doi.org/10.1007/s10476-018-0505-5

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  • DOI: https://doi.org/10.1007/s10476-018-0505-5

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