Measure theory and pseudo almost periodic automorphic functions: new developments and applications

Joël Blot (1) , Philippe Cieutat (2) , Khalil Ezzinbi (3)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LMV - Laboratoire de Mathématiques de Versailles
3 Département de mathématiques [FSSM]

In this work, we establish a new concept of weighted almost automorphic function using the measure theory. We present new results on weighted ergodic functions like completeness and composition theorems. The theory of this work generalizes the clasical results on weighted almost periodic and automorphic functions. For illustration, we provide some applications for evolution equations which include reaction-diffusion systems and partial functional differential equations.

Mots clés: measure theory; ergocity; mu-pseudo almost automorphic function; completeness; composition theorem; evolution equation; reaction-diffusion system; partial functional differential equation

Domaines: Equations aux dérivées partielles [math.AP]

Joël Blot, Philippe Cieutat, Khalil Ezzinbi. Measure theory and pseudo almost periodic automorphic functions: new developments and applications. Nonlinear Analysis: Theory, Methods and Applications, 2012, 75, pp.2426-2447. ⟨10.1016/j.na.2011.10.041⟩. ⟨hal-00664739⟩