New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results 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]

The aim of this work is to present new approach to study weighted pseudo almost periodic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions like completeness and composition theorems. The theory of this work generalizes the classical results on weighted pseudo almost periodic functions. For illustration, we provide some applications for evolution equations which include reaction diffusion system and partial functional differential equations.

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

Domaines: Equations aux dérivées partielles [math.AP]

Joël Blot, Philippe Cieutat, Khalil Ezzinbi. New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications. Applicable Analysis, 2011, volume 2011, iFirst, pp.1-34. ⟨10.1080/00036811.2011.628941⟩. ⟨hal-00662508⟩