On Hartman almost periodic functions

• Autorzy: Guy Cohen , Viktor Losert
• Języki publikacji: EN

Abstrakty

EN

We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in $ℝ^{d}$ or $ℤ^{d}$. 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.

Kategorie tematyczne

• 42A75: Classical almost periodic functions, mean periodic functions
• 42B35: Function spaces arising in harmonic analysis
• 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
• 11K70: Harmonic analysis and almost periodicity

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 173
• Numer: 1
• Strony: 81-101

Daty

wydano

2006

Twórcy

autor

Guy Cohen

• Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel

autor

Viktor Losert

• Fakultät für Mathematik, Universität Wien, Nordbergstr. 15, A-1090 Wien, Austria

Identyfikatory

DOI

10.4064/sm173-1-6