Hamid Bounit, Ahmed Fadili
Abstract:
We introduce the Favard spaces for resolvent families, extending some
well-known theorems for semigroups. Furthermore, we show the relationship
between these Favard spaces and the
-admissibility
of control
operators for scalar Volterra linear systems in Banach spaces, extending
some results in [22]. Assuming that the kernel a(t) is
a creep function which satisfies
,
we prove an analogue
version of the Weiss conjecture for scalar Volterra linear systems
when p=1. To this end, we also show that the finite-time and infinite-time
(resp. finite-time and uniform finite-time)
-admissibility
coincide for exponentially stable resolvent families (reps. for reflexive
state space), extending well-known results for semigroups.
Submitted March 22, 2014. Published February 12, 2015.
Math Subject Classifications: 45D05, 45E05, 45E10, 47D06.
Key Words: Semigroups; Volterra integral equations; resolvent family;
Favard space; admissibility.
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Hamid Bounit Department of Mathematics, Faculty of Sciences Ibn Zohr University, BP 8106 Agadir 80 000, Morocco email: h.bounit@uiz.ac.ma | |
Ahmed Fadili Department of Mathematics, Faculty of Sciences Ibn Zohr University, BP 8106 Agadir 80 000, Morocco email: ahmed.fadili@edu.uiz.ac.ma |
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