Simultaneous observability of infinitely many strings and beams

Vilmos Komornik; Anna Chiara Lai; Paola Loreti; Vilmos Komornik; Anna Chiara Lai; Paola Loreti

doi:10.3934/nhm.2020017

Networks and Heterogeneous Media

2020, Volume 15, Issue 4: 633-652. doi: 10.3934/nhm.2020017

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Simultaneous observability of infinitely many strings and beams

1.
College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, People's Republic of China
2.
Département de mathématique, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg Cedex, France
3.
Sapienza Università di Roma, Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Via A. Scarpa, 16, 00161, Roma, Italy

Received: 01 June 2019 Revised: 01 June 2020 Published: 13 August 2020
Primary: 93B07; Secondary: 35L05, 74K10, 42A99

We investigate the simultaneous observability of infinite systems of vibrating strings or beams having a common endpoint where the observation is taking place. Our results are new even for finite systems because we allow the vibrations to take place in independent directions. Our main tool is a vectorial generalization of some classical theorems of Ingham, Beurling and Kahane in nonharmonic analysis.
- Fourier series,
- non-harmonic analysis,
- wave equation,
- strings,
- beams,
- observability
Citation: Vilmos Komornik, Anna Chiara Lai, Paola Loreti. Simultaneous observability of infinitely many strings and beams[J]. Networks and Heterogeneous Media, 2020, 15(4): 633-652. doi: 10.3934/nhm.2020017

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Abstract

We investigate the simultaneous observability of infinite systems of vibrating strings or beams having a common endpoint where the observation is taking place. Our results are new even for finite systems because we allow the vibrations to take place in independent directions. Our main tool is a vectorial generalization of some classical theorems of Ingham, Beurling and Kahane in nonharmonic analysis.

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