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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## On Hartman almost periodic functions

### Tom 173 / 2006

Studia Mathematica 173 (2006), 81-101 MSC: Primary 42B35; Secondary 11K70, 42A75, 43A60. DOI: 10.4064/sm173-1-6

#### Streszczenie

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.

#### Autorzy

• Guy CohenInstitute of Mathematics
Hebrew University
Givat Ram
Jerusalem 91904, Israel
e-mail
• Viktor LosertFakultät für Mathematik
Universität Wien
Nordbergstr. 15
A-1090 Wien, Austria
e-mail

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