Comptes Rendus
no. 3
Elastic and piezoelectric waveguides may have infinite number of gaps in their spectra
[Les guides d'ondes élastiques et piézoélectriques peuvent avoir un nombre infini de lacunes dans leur spectre]
Sergei A. Nazarov1, 2, 3 ; Jari Taskinen4 
1 Saint-Petersburg State University, Universitetskaya nab., 7–9, St. Petersburg, 199034, Russia
2 Peter the Great Saint-Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, St. Petersburg, 195251, Russia
3 Institute of Problems of Mechanical Engineering RAS, V.O., Bolshoj pr., 61, St. Petersburg, 199178, Russia
4 University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, 00014 Helsinki, Finland
Comptes Rendus. Mécanique, Volume 344 (2016) no. 3, pp. 190-194.

Nous considérons des guides d'ondes élastiques et piézoélectriques réalisés à partir de perles identiques agencées de façon périodique le long d'un rayon convergeant à l'infini. Nous montrons que le spectre essentiel est une suite croissante positive non bornée. Cela prouve l'existence d'un nombre infini de trous spectraux.

We consider elastic and piezoelectric waveguides composed from identical beads threaded periodically along a spoke converging at infinity. We show that the essential spectrum constitutes a non-negative monotone unbounded sequence and thus has infinitely many spectral gaps.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2015.12.004
Keywords: Waveguide, Elasticity, Piezoelectricity, Essential spectrum, Spectral gap, Singular Weyl sequence, Parametrix
Mot clés : Guide d'ondes, Élasticité, Piézoélectricité, Spectre essentiel, Troux spectraux, Suite de Weyl, Paramétrix
Sergei A. Nazarov 1, 2, 3 ; Jari Taskinen 4

1 Saint-Petersburg State University, Universitetskaya nab., 7–9, St. Petersburg, 199034, Russia
2 Peter the Great Saint-Petersburg State Polytechnical University, Polytechnicheskaya ul., 29, St. Petersburg, 195251, Russia
3 Institute of Problems of Mechanical Engineering RAS, V.O., Bolshoj pr., 61, St. Petersburg, 199178, Russia
4 University of Helsinki, Department of Mathematics and Statistics, P.O. Box 68, 00014 Helsinki, Finland 
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     author = {Sergei A. Nazarov and Jari Taskinen},
     title = {Elastic and piezoelectric waveguides may have infinite number of gaps in their spectra},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {190--194},
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     number = {3},
     year = {2016},
     doi = {10.1016/j.crme.2015.12.004},
     language = {en},
}
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Sergei A. Nazarov; Jari Taskinen. Elastic and piezoelectric waveguides may have infinite number of gaps in their spectra. Comptes Rendus. Mécanique, Volume 344 (2016) no. 3, pp. 190-194. doi : 10.1016/j.crme.2015.12.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.12.004/

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