Abstract
Motivated by and extending a theorem of Reiter on sets of synthesis in \(\mathbb {R}^N\), we establish a general result for Fourier algebras of locally compact groups, even in the wider context of regular, semisimple and Tauberian commutative Banach algebras, which contains Reiter’s theorem as a special case and explains why it holds. In addition, we give a number of examples and several further results on weak spectral sets.
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Communicated by A. Constantin.
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Kaniuth, E., Ülger, A. On a theorem of Reiter and spectral synthesis. Monatsh Math 181, 839–853 (2016). https://doi.org/10.1007/s00605-016-0885-1
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DOI: https://doi.org/10.1007/s00605-016-0885-1
Keywords
- Locally compact group
- Fourier algebra
- Set of synthesis
- Ditkin set
- Commutative Banach algebra
- Structure space
- Weak spectral set