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Spectra of Beurling algebras of abelian groups
Abstract
We give a complete classification of all sets which are spectra of Beurling algebras of any locally compact abelian group, parametrizing them by compact convex sets in the dual of a certain locally convex vector space generated by the group. Hence, for example, a finitely generated free abelian group may enjoy a more complicated range of such spectra than the does rational numbers.
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BibTeX
@misc{spronk2026spectra,
title = {{Spectra of Beurling algebras of abelian groups}},
author = {Nico Spronk and Zhihao Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03437},
eprint = {2611.03437},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03437},
}
RIS
TY - UNPB
TI - Spectra of Beurling algebras of abelian groups
AU - Nico Spronk
AU - Zhihao Zhang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03437
UR - https://arxiv.org/abs/2611.03437
AB - We give a complete classification of all sets which are spectra of Beurling algebras of any locally compact abelian group, parametrizing them by compact convex sets in the dual of a certain locally convex vector space generated by the group. Hence, for example, a finitely generated free abelian group may enjoy a more complicated range of such spectra than the does rational numbers.
ER -