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Comptes Rendus Mathématique
Volume 337, n° 1
pages 19-24 (juillet 2003)
Doi : 10.1016/S1631-073X(03)00251-6
Received : 5 December 2002 ;  accepted : 20 May 2003
Generalized Riesz basis property in the analysis of neutral type systems

Rabah  Rabah a ,  Grigory M.  Sklyar b ,  Alexander V.  Rezounenko c
aIRCCyN UMR 6597, 1, rue de la Noë, PB 92101, 44321 Nantes cedex 3, France 
bInstitute of Mathematics, University of Szczecin, 70-451 Szczecin, Wielkopolska 15, Poland 
cDepartment of Mechanics and Mathematics, Kharkov University, 4 Svobody sqr., Kharkov, 61077, Ukraine 


The functional differential equation of neutral type is studied. We consider the corresponding operator model in Hilbert space   and prove that there exists a sequence of invariant finite-dimensional subspaces which constitute a Riesz basis in  . We also give an example emphasizing that the generalized eigenspaces do not form a Riesz basis. To cite this article: R. Rabah et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).


On étudie une équation différentielle fonctionnelle de type neutre. Nous considérons le modèle opérationnel dans l'espace de Hilbert   et montrons qu'il existe dans cet espace une base de Riesz de sous-espaces de dimensions finies invariants par l'opérateur générateur infinitésimal du système. Nous donnons également un exemple précisant qu'il n'existe pas de base de Riesz de sous-espaces propres. Pour citer cet article : R. Rabah et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).

© 2003  Académie des sciences@@#104156@@

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