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

In this paper we prove that the system of generalized eigenvectors of the operator (I + εK)−1 × d4/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.  2003 Elsevier Inc. All rights reserved.