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Fourier Transforms of Distributions and Hausdorff Measures

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Abstract

Consider a distribution whose support has Hausdorff \(h\)-measure zero. How fast can its Fourier coefficients decay to zero? If \(h\) is close to linear, we can improve on known results by a factor of about \((\log n)^{-1/2}\).

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  1. Centre for Mathematical Sciences, DPMMS, Clarkson Road, Cambridge, UK

    T. W. Körner

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  1. T. W. Körner
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Correspondence to T. W. Körner.

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Communicated by John J. Benedetto.

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Körner, T.W. Fourier Transforms of Distributions and Hausdorff Measures. J Fourier Anal Appl 20, 547–565 (2014). https://doi.org/10.1007/s00041-014-9328-3

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  • DOI: https://doi.org/10.1007/s00041-014-9328-3

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