Comptes Rendus
Elastic and piezoelectric waveguides may have infinite number of gaps in their spectra
Comptes Rendus. Mécanique, Volume 344 (2016) no. 3, pp. 190-194.

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.

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.

Published online:
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
     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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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.

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