Convolutions in \((\mu,\nu)\)-pseudo-almost periodic and \((\mu,\nu)\)-pseudo-almost automorphic function spaces and applications to solve integral equations

David Békollè; Khalil Ezzinbi; Samir Fatajou; Duplex Elvis Houpa Danga; Fritz Mbounja Béssémè

doi:10.4067/S0719-06462021000100063

DOI:

https://doi.org/10.4067/S0719-06462021000100063

Abstract

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.

Keywords

Measure theory , \(\mu\), \(\nu\)-ergodic , \(\mu\), \(\nu\)-pseudo almost periodic and automorphic functions , Evolution families , nonautonomous equations , neutral systems

David Békollè Department of Mathematics, Faculty of Science, University of Ngaoundéré P.O. Box 454, Ngaoundéré, Cameroon.
Khalil Ezzinbi Department of Mathematics, Faculty of Science Semlalia, Cadi Ayyad University, B.P. 2390 Marrakesh, Morocco.
Samir Fatajou Department of Mathematics, Faculty of Science Semlalia, Cadi Ayyad University, B.P. 2390 Marrakesh, Morocco.
Duplex Elvis Houpa Danga Department of Mathematics, Faculty of Science, University of Ngaoundéré P.O. Box 454, Ngaoundéré, Cameroon.
Fritz Mbounja Béssémè Department of Mines and Geology, School of Geology and Mining Engineering, University of Ngaoundéré P.O. Box 454, Ngaoundéré, Cameroon.

Pages: 63–85
Date Published: 2021-04-14
Vol. 23 No. 1 (2021)

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