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Quasicrystals and Control Theory

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Analysis and Geometry

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 127))

Abstract

Cross-fertilization between control theory and irregular sampling is illustrated by two examples. Salah Baouendi applauded new ideas and welcomed new cultures. Interdisciplinary research is crossing frontiers, as Baouendi did all along his life. Two examples of cross-fertilization between harmonic analysis and control theory will be discussed in this homage. In 1983 Jacques-Louis Lions raised a problem in control theory. The solution I gave was grounded on a theorem on trigonometric sums proved by Arne Beurling. This will be our first example. The second example goes the other way around. A problem on trigonometric sums is solved using tools from control theory. Frontiers are erased as Baouendi wished.

In memory of M. Salah Baouendi

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Acknowledgments

I am very grateful to Linda Rothschild for her help and to the anonymous referee for her/his constructive criticism.

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Authors and Affiliations

  1. CMLA, ENS-Cachan, 94235, Cachan Cedex, France

    Yves Meyer

Authors
  1. Yves Meyer
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Correspondence to Yves Meyer .

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Editors and Affiliations

  1. Département de Mathématiques, Université de Sfax, Sfax, Tunisia

    Ali Baklouti

  2. LAMAV, ISTV2, Université de Valenciennes, Valenciennes cedex 9, France

    Aziz El Kacimi

  3. Department of Mathematics and Statistics, The American University of Sharjah, Sharjah, Utd.Arab.Emir.

    Sadok Kallel

  4. Texas A&M University at Qatar, Doha, Qatar

    Nordine Mir

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Meyer, Y. (2015). Quasicrystals and Control Theory. In: Baklouti, A., El Kacimi, A., Kallel, S., Mir, N. (eds) Analysis and Geometry. Springer Proceedings in Mathematics & Statistics, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-319-17443-3_12

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