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Quasicrystals and Control Theory

  • Yves Meyer
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (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.

Keywords

Control theory Quasicrystals Irregular sampling 

2010 Mathematics Subject Classification

Primary 42A75 Secondary 94A20 

Notes

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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.CMLAENS-CachanCachan CedexFrance

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