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Thin sets of integers in harmonic analysis and p-stable random fourier series

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Abstract

We investigate the behaviour of some thin sets of integers defined through random trigonometric polynomials when one replaces Gaussian or Rademacher variables with p-stable ones, 1 < p < 2. We show that in one case, this behaviour is essentially the same as in the Gaussian case, whereas in another case, it is entirely different.

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Authors and Affiliations

  1. Fédération CNRS Nord-Pas-de-Calais FR 2956 Faculté Jean Perrin, Univ. Lille Nord de France U-Artois, Laboratoire de Mathématiques de Lens EA 2462, rue Jean Souvraz SP 18, F-62 300, Lens, France

    Pascal Lefèvre & Daniel Li

  2. USTL, Laboratoire Paul Painlevé U.M.R. CNRS 8524, Univ Lille Nord de France, F-59 655, Villeneuve, D’Ascq Cedex, France

    Hervé Queffélec

  3. Facultad de Matemáticas, Departamento de Análisismatemático, Universidad de Sevilla, Apartado de Correos 1160, 41 080, Sevilla, Spain

    Luis Rodríguez-Piazza

Authors
  1. Pascal Lefèvre
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  2. Daniel Li
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  3. Hervé Queffélec
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  4. Luis Rodríguez-Piazza
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Corresponding author

Correspondence to Pascal Lefèvre.

Additional information

Dedicated to the memories of Daniel Rider and Walter Rudin

This work is partially supported by Spanish project MTM2006-05622. L. Rodríguez-Piazza is partially supported by Spanish research projects MTM2006-05622 and MTM2009-08934.

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Lefèvre, P., Li, D., Queffélec, H. et al. Thin sets of integers in harmonic analysis and p-stable random fourier series. JAMA 115, 187–211 (2011). https://doi.org/10.1007/s11854-011-0027-6

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  • DOI: https://doi.org/10.1007/s11854-011-0027-6

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