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2012 Polynomial functions and spectral synthesis on Abelian groups
Laszlo Szekelyhid
Banach J. Math. Anal. 6(1): 124-131 (2012). DOI: 10.15352/bjma/1337014670

Abstract

Spectral synthesis deals with the description of translation invariant function spaces. It turns out that the basic building blocks of this description are the exponential monomials, which are built up from exponential functions and polynomial functions. The author collaborated with Laczkovich [Math. Proc. Cambridge Philos. Soc. 143 (2007), no. 1, 103--120] proved that spectral synthesis holds on an Abelian group if and only if the torsion free rank of the group is finite. The author [Aequationes Math. 70 (2005), no. 1-2, 122--130] showed that the torsion free rank of an Abelian group is strongly related to the properties of polynomial functions on the group. Here we show that spectral synthesis holds on an Abelian group if and only if the ring of polynomial functions on the group is Noetherian.

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Laszlo Szekelyhid. "Polynomial functions and spectral synthesis on Abelian groups." Banach J. Math. Anal. 6 (1) 124 - 131, 2012. https://doi.org/10.15352/bjma/1337014670

Information

Published: 2012
First available in Project Euclid: 14 May 2012

MathSciNet: MR2862548
Digital Object Identifier: 10.15352/bjma/1337014670

Subjects:
Primary: 43A45
Secondary: 16P40 , 39A70

Keywords: Noetherian ring , Polynomial function , spectral synthesis

Rights: Copyright © 2012 Tusi Mathematical Research Group

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Vol.6 • No. 1 • 2012
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