Local spectral synthesis on Abelian groups

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• 作者：Miklós Laczkovich (1) (2)
  
• 关键词：spectral synthesis ; polynomial ; exponential function ; 43A45 ; 43A70 ; 13F20
• 刊名：Acta Mathematica Hungarica
• 出版年：2014
• 出版时间：August 2014
• 年：2014
• 卷：143
• 期：2
• 页码：313-329
• 全文大小：567 KB
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• 作者单位：Miklós Laczkovich (1) (2)
  
  1. Department of Analysis, E?tv?s Loránd University, Budapest, Pázmány Péter sétány 1/C, 1117, Hungary
  2. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England
  
• ISSN：1588-2632

文摘

We say that a complex valued function defined on an Abelian group?G is a local polynomial, if its restriction to every finitely generated subgroup of?G is a polynomial. We prove that local spectral synthesis (that is, spectral synthesis using local polynomials instead of polynomials) holds on every Abelian group having countable torsion free rank. More precisely, there is a cardinal ω 1?em class="a-plus-plus">κ? ω such that local spectral synthesis holds on an Abelian group?G if and only if the torsion free rank of?G is less than?κ.