Convolutions in \((\mu,\nu)\)-pseudo-almost periodic and \((\mu,\nu)\)-pseudo-almost automorphic function spaces and applications to solve integral equations
DOI:
https://doi.org/10.4067/S0719-06462021000100063Keywords:
Measure theory, \(\mu\), \(\nu\)-ergodic, \(\mu\), \(\nu\)-pseudo almost periodic and automorphic functions, Evolution families, nonautonomous equations, neutral systemsAbstract
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.
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