Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations
In this paper we give sufficient conditions on $k\in L^1(\mathbb{R})$ and the positive measures $\mu$, $\nu$ such that the doubly-measure pseudo-almost periodic (respectively, doubly-measure pseudo-almost automorphic) function spaces are invariant by the convolution product $\zeta f=k\ast f$. We pro...
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Universidad de La Frontera
2021-04-01
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| Online Access: | http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2598/2052 |
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doaj-11fbf7aade6f4b709dd5edf993ec40fd2021-06-14T19:17:06ZengUniversidad de La FronteraCubo0716-77760719-06462021-04-01231638510.4067/S0719-06462021000100063Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equationsDavid Békollè0Khalil Ezzinbi1Samir Fatajou2https://orcid.org/0000-0001-5959-098XDuplex Elvis Houpa Danga3https://orcid.org/0000-0003-4779-5800Fritz Mbounja Béssémè4https://orcid.org/0000-0002-6052-6755Department of Mathematics, Faculty of Science, University of Ngaoundéré P.O. Box 454, Ngaoundéré, Cameroon.Department of Mathematics, Faculty of Science Semlalia, Cadi Ayyad University, B.P. 2390 Marrakesh, Morocco.Department of Mathematics, Faculty of Science Semlalia, Cadi Ayyad University, B.P. 2390 Marrakesh, Morocco.Department of Mathematics, Faculty of Science, University of Ngaoundéré P.O. Box 454, Ngaoundéré, Cameroon.Department of Mines and Geology, School of Geology and Mining Engineering, University of Ngaoundéré P.O. Box 454, Ngaoundéré, Cameroon.In this paper we give sufficient conditions on $k\in L^1(\mathbb{R})$ and the positive measures $\mu$, $\nu$ such that the doubly-measure pseudo-almost periodic (respectively, doubly-measure pseudo-almost automorphic) function spaces are invariant by the convolution product $\zeta f=k\ast f$. We provide an appropriate example to illustrate our convolution results. As a consequence, we study under Acquistapace-Terreni conditions and exponential dichotomy, the existence and uniqueness of $\left( \mu,\nu\right)$- pseudo-almost periodic (respectively, $\left( \mu,\nu\right)$- pseudo-almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces like neutral systems.http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2598/2052measure theoryμ-ν-ergodicμ-ν -pseudo almost periodic and automorphic functionsevolution familiesnonautonomous equationsneutral systems |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
David Békollè Khalil Ezzinbi Samir Fatajou Duplex Elvis Houpa Danga Fritz Mbounja Béssémè |
| spellingShingle |
David Békollè Khalil Ezzinbi Samir Fatajou Duplex Elvis Houpa Danga Fritz Mbounja Béssémè Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations Cubo measure theory μ-ν-ergodic μ-ν -pseudo almost periodic and automorphic functions evolution families nonautonomous equations neutral systems |
| author_facet |
David Békollè Khalil Ezzinbi Samir Fatajou Duplex Elvis Houpa Danga Fritz Mbounja Béssémè |
| author_sort |
David Békollè |
| title |
Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations |
| title_short |
Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations |
| title_full |
Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations |
| title_fullStr |
Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations |
| title_full_unstemmed |
Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations |
| title_sort |
convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations |
| publisher |
Universidad de La Frontera |
| series |
Cubo |
| issn |
0716-7776 0719-0646 |
| publishDate |
2021-04-01 |
| description |
In this paper we give sufficient conditions on $k\in L^1(\mathbb{R})$ and the positive measures $\mu$, $\nu$ such that the doubly-measure pseudo-almost periodic (respectively, doubly-measure pseudo-almost automorphic) function spaces are invariant by the convolution product $\zeta f=k\ast f$. We provide an appropriate example to illustrate our convolution results. As a consequence, we study under Acquistapace-Terreni conditions and exponential dichotomy, the existence and uniqueness of $\left( \mu,\nu\right)$- pseudo-almost periodic (respectively, $\left( \mu,\nu\right)$- pseudo-almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces like neutral systems. |
| topic |
measure theory μ-ν-ergodic μ-ν -pseudo almost periodic and automorphic functions evolution families nonautonomous equations neutral systems |
| url |
http://revistas.ufro.cl/ojs/index.php/cubo/article/view/2598/2052 |
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