## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On the Admissible Control operators for Linear and Bilinear Systems and the Favard Spaces

#### 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 4 (2014), 711-732.

Dates
First available in Project Euclid: 23 October 2014

https://projecteuclid.org/euclid.bbms/1414091010

Digital Object Identifier
doi:10.36045/bbms/1414091010

Mathematical Reviews number (MathSciNet)
MR3271328

Zentralblatt MATH identifier
1301.93046

#### Citation

Maragh, F.; Bounit, H.; Fadili, A.; Hammouri, H. On the Admissible Control operators for Linear and Bilinear Systems and the Favard Spaces. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 4, 711--732. doi:10.36045/bbms/1414091010. https://projecteuclid.org/euclid.bbms/1414091010