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New Trends in Applied Harmonic Analysis, Volume 2 pp 129–157Cite as

Birkhäuser

Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets

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Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

This is a survey on recent developments on the Hausdorff dimension of projections and intersections for general subsets of Euclidean spaces, with an emphasis on estimates of the Hausdorff dimension of exceptional sets and on restricted projection families. We shall also discuss relations between projections and Hausdorff dimension of Besicovitch sets.

The author was supported by the Academy of Finland through the Finnish Center of Excellence in Analysis and Dynamics Research.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Pertti Mattila

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  1. Pertti Mattila
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Editors and Affiliations

  1. Vanderbilt University, Nashville, TN, USA

    Akram Aldroubi

  2. Department of Mathematics (FCEyN), Universidad de Buenos Aires, Buenos Aires, Argentina

    Carlos Cabrelli

  3. Department of Mathematics (LAMA), Université Paris-Est Créteil, Creteil, Paris, France

    Stéphane Jaffard

  4. Department of Mathematics (FCEyN), Universidad de Buenos Aires, Buenos Aires, Argentina

    Ursula Molter

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Mattila, P. (2019). Hausdorff Dimension, Projections, Intersections, and Besicovitch Sets. In: Aldroubi, A., Cabrelli, C., Jaffard, S., Molter, U. (eds) New Trends in Applied Harmonic Analysis, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-32353-0_6

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