Tobias Habacker, Title: Besicovitch-almost periodic functions as weights in ergodictheorems for locally compact amenable groupsBesicovitch-almost periodic functions as weights in ergodictheorems for locally compact amenable groups

Originally dating back to Harald Bohr, different concepts of almost periodic functions havebeen introduced by several authors. On locally compact abelian groups, Lenz, Spindeler andStrungaru (2020) defined Besicovitch-almost periodicity and gave an intrinsic characterisation for f ∈ L^2_{loc}(G) belonging to the space Bap^2_F (G).Already investigated by Følner in 1957, we will explore this theory in the setting of apossibly nonabelian group G and generalise the characterisation of Bap^2_F (G). The maindifference to the abelian case is rooted in the representation theory of G: If G is abelian,every irreducible representation of G is of dimension one, which is not true in the general case.Following Lin and Olsen (2011), we further show a weighted mean ergodic theorem, usingBesicovitch-a.p. functions as weights. Applying a maximal inequality, one obtains a pointwiseresult. Finally this can then be applied to give a description of the JdLG-decomposition forthe dynamical system arising from a measure preserving action of G on some measure space X in terms of the representation theory of G.