Bulletin of the Belgian Mathematical Society - Simon Stevin
- Bull. Belg. Math. Soc. Simon Stevin
- Volume 21, Number 4 (2014), 711-732.
On the Admissible Control operators for Linear and Bilinear Systems and the Favard Spaces
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  (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  and Berrahmoune  and are applied to diffusion equations of fractional order time distributed order.
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 4 (2014), 711-732.
First available in Project Euclid: 23 October 2014
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35R15: Partial differential equations on infinite-dimensional (e.g. function) spaces (= PDE in infinitely many variables) [See also 46Gxx, 58D25] 39A14: Partial difference equations 32A70: Functional analysis techniques [See mainly 46Exx] 93C25: Systems in abstract spaces 93C20: Systems governed by partial differential equations
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