Favard spaces and admissibility for Volterra systems with scalar kernel
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 $L^p$-admissibility of control operators for scalar Volterra linear systems in Banach spaces, extending some results...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/42/abstr.html |
| _version_ | 1811201869751517184 |
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| author | Hamid Bounit Ahmed Fadili |
| author_facet | Hamid Bounit Ahmed Fadili |
| author_sort | Hamid Bounit |
| collection | DOAJ |
| description | 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 $L^p$-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 $a(0^+)>0$, 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) $L^{1}$-admissibility
coincide for exponentially stable resolvent families (reps. for reflexive
state space), extending well-known results for semigroups. |
| first_indexed | 2024-04-12T02:29:10Z |
| format | Article |
| id | doaj.art-bb96d603ea8c4130b7b7cf2abba7d45d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T02:29:10Z |
| publishDate | 2015-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-bb96d603ea8c4130b7b7cf2abba7d45d2022-12-22T03:51:52ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-02-01201542,121Favard spaces and admissibility for Volterra systems with scalar kernelHamid Bounit0Ahmed Fadili1 Ibn Zohr Univ., Agadir, Morocco Ibn Zohr Univ., Agadir, Morocco 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 $L^p$-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 $a(0^+)>0$, 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) $L^{1}$-admissibility coincide for exponentially stable resolvent families (reps. for reflexive state space), extending well-known results for semigroups.http://ejde.math.txstate.edu/Volumes/2015/42/abstr.htmlSemigroupsVolterra integral equationsresolvent familyFavard spaceadmissibility |
| spellingShingle | Hamid Bounit Ahmed Fadili Favard spaces and admissibility for Volterra systems with scalar kernel Electronic Journal of Differential Equations Semigroups Volterra integral equations resolvent family Favard space admissibility |
| title | Favard spaces and admissibility for Volterra systems with scalar kernel |
| title_full | Favard spaces and admissibility for Volterra systems with scalar kernel |
| title_fullStr | Favard spaces and admissibility for Volterra systems with scalar kernel |
| title_full_unstemmed | Favard spaces and admissibility for Volterra systems with scalar kernel |
| title_short | Favard spaces and admissibility for Volterra systems with scalar kernel |
| title_sort | favard spaces and admissibility for volterra systems with scalar kernel |
| topic | Semigroups Volterra integral equations resolvent family Favard space admissibility |
| url | http://ejde.math.txstate.edu/Volumes/2015/42/abstr.html |
| work_keys_str_mv | AT hamidbounit favardspacesandadmissibilityforvolterrasystemswithscalarkernel AT ahmedfadili favardspacesandadmissibilityforvolterrasystemswithscalarkernel |