On Hartman almost periodic functions

Guy Cohen¹ ; Viktor Losert²

¹Institute of Mathematics Hebrew University Givat Ram Jerusalem 91904, Israel
²Fakultät für Mathematik Universität Wien Nordbergstr. 15 A-1090 Wien, Austria

Studia Mathematica, Tome 173 (2006) no. 1, pp. 81-101

Résumé

We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in $\mathbb R^d$ or $\mathbb Z^d$. We consider the behavior of their Fourier–Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces and general averaging sequences of subsets. We extend results of Urbanik to locally compact abelian groups.

Détail

DOI : 10.4064/sm173-1-6

Keywords: consider multi dimensional hartman almost periodic functions sequences defined respect different averaging sequences subsets mathbb mathbb consider behavior their fourier bohr coefficients their spectrum depending particular averaging sequence demonstrate dependence several examples extensions compactly generated locally compact abelian groups considered define generalized marcinkiewicz spaces based arbitrary measure spaces general averaging sequences subsets extend results urbanik locally compact abelian groups