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october 2014 On the Admissible Control operators for Linear and Bilinear Systems and the Favard Spaces
F. Maragh, H. Bounit, A. Fadili, H. Hammouri
Bull. Belg. Math. Soc. Simon Stevin 21(4): 711-732 (october 2014). DOI: 10.36045/bbms/1414091010

Abstract

The objective of this work is to give some relationship between the Favard spaces and the $p$-admissibility (resp. $(p,q)$-admissibility) of unbounded control operators for linear (resp; bilinear) systems in Banach spaces. For linear case, this enables to give a simple identification of the space of the $1-$admissible control operators in Banach space and it enables us to extend the result of Weiss [29] (for $p=1$) on reflexive Banach spaces to a general situation. This result is applied to boundary control systems. The results obtained for bilinear systems generalize those given in Idrissi [16] and Berrahmoune [2] and are applied to diffusion equations of fractional order time distributed order.

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F. Maragh. H. Bounit. A. Fadili. H. Hammouri. "On the Admissible Control operators for Linear and Bilinear Systems and the Favard Spaces." Bull. Belg. Math. Soc. Simon Stevin 21 (4) 711 - 732, october 2014. https://doi.org/10.36045/bbms/1414091010

Information

Published: october 2014
First available in Project Euclid: 23 October 2014

zbMATH: 1301.93046
MathSciNet: MR3271328
Digital Object Identifier: 10.36045/bbms/1414091010

Subjects:
Primary: 32A70 , 34K30 , 35R15 , 39A14 , 93C20 , 93C25

Keywords: abstract linear (bilinear) control systems , Admissibility , boundary control systems , Favard spaces , Infinite-dimensional systems , semigroups , unbounded linear (bilinear) control systems

Rights: Copyright © 2014 The Belgian Mathematical Society

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Vol.21 • No. 4 • october 2014
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