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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 

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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).

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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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