A remark on the geometry of spaces of functions with prime frequencies
| Autor: | Pascal Lefèvre, Olivier Ramaré, Étienne Matheron |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques de Lens (LML), Université d'Artois (UA), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille |
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Discrete mathematics
General Mathematics 010102 general mathematics Prime numbers Prime number Geometry disk algebra Fourier spectrum [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Thin set Prime (order theory) continuous functions Integer thin sets AMS Condensed Matter::Superconductivity 0103 physical sciences 010307 mathematical physics 0101 mathematics Algebra over a field Disk algebra Mathematics |
| Zdroj: | Acta Mathematica Hungarica Acta Mathematica Hungarica, Springer Verlag, 2014, 143 (1), pp.75-80. ⟨10.1007/s10474-014-0408-2⟩ Acta Mathematica Hungarica, 2014, 143 (1), pp.75-80. ⟨10.1007/s10474-014-0408-2⟩ |
| ISSN: | 0236-5294 1588-2632 |
| DOI: | 10.1007/s10474-014-0408-2⟩ |
| Popis: | For any positive integer r, denote by \({\mathcal{P}_{r}}\) the set of all integers \({\gamma \in \mathbb{Z}}\) having at most r prime divisors. We show that \({C_{\mathcal{P}_{r}}(\mathbb{T})}\), the space of all continuous functions on the circle \({\mathbb{T}}\) whose Fourier spectrum lies in \({\mathcal{P}_{r}}\), contains a complemented copy of \({\ell^{1}}\). In particular, \({C_{\mathcal{P}_{r}}(\mathbb{T})}\) is not isomorphic to \({C(\mathbb{T})}\), nor to the disc algebra \({A(\mathbb{D})}\). A similar result holds in the L1 setting. |
| Databáze: | OpenAIRE |
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