On an Riesz basis of generalized eigenvectors of the nonselfadjoint problem deduced from a perturbation method for sound radiation by a vibrating plate in a light fluid |
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| Authors: | Aref Jeribi Abdelkader Intissar |
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| Institution: | a Département de Mathématiques, Faculté des Sciences de Sfax, Université de Sfax, Route de Soukra, Km 3.5, B.P. 802, 3018 Sfax, Tunisia
b Département de Mathématiques, Equipe d'Analyse Spectrale, CNRS URA 2053, Université de Corse, Quartier Grossetti, B.P. 52, 20250 Corte, France |
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| Abstract: | In this paper we prove that the system of generalized eigenvectors of the operator (I+εK)−1d4/dx4 forms a Riesz basis of L2(]−L,L) where K is the integral operator with kernel the Hankel function of the first kind and order 0. This operator was introduced in J. Sound Vibration 177 (1994) 259-275. We give positive answers to the hypotheses posed in that article. |
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