Jamison sequences in countably infinite discrete Abelian groups
We extend the definition of Jamison sequences in the context of topological abelian groups. We then study these sequences when the group is discrete and countably infinite. An arithmetical characterization of such sequences is obtained, extending the result of Badea and Grivaux [2] about Jamison seq...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2016
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| Sorozat: | Acta scientiarum mathematicarum
82 No. 3-4 |
| Kulcsszavak: | Pontspektrum, Jamison sor, diszkrét Abel-csoport, Haar mérték, Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-015-020-3 |
| Online Access: | http://acta.bibl.u-szeged.hu/46322 |
| Tartalmi kivonat: | We extend the definition of Jamison sequences in the context of topological abelian groups. We then study these sequences when the group is discrete and countably infinite. An arithmetical characterization of such sequences is obtained, extending the result of Badea and Grivaux [2] about Jamison sequences of integers. In particular, we prove that the sequence consisting in all the elements of the group is a Jamison sequence. In the opposite, a sequence which generates a subgroup of infinite index in the group is never a Jamison sequence. We also generalize a result of Nikolskii by showing that the growth of the norms of a representation is influenced by the Haar measure of its unimodular point spectrum. |
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| Terjedelem/Fizikai jellemzők: | 481-508 |
| ISBN: | 0001-6969 |