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April 2016 On the powers of maximal ideals in the measure algebra
László Székelyhidi
Banach J. Math. Anal. 10(2): 385-399 (April 2016). DOI: 10.1215/17358787-3495693

Abstract

In this paper, we describe the powers of maximal ideals in the measure algebra of some locally compact Abelian groups in terms of the derivatives of the Fourier–Laplace transform of compactly supported measures. We show that if the locally compact Abelian group has sufficiently many real characters, then all derivatives of the Fourier–Laplace transform of a measure at some point of its spectrum completely characterize the measure. We also show that the derivatives of the Fourier–Laplace transform of a measure can be used to describe the powers of the maximal ideals corresponding to the points of the spectrum of the measure on discrete Abelian groups with finite torsion-free rank.

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László Székelyhidi. "On the powers of maximal ideals in the measure algebra." Banach J. Math. Anal. 10 (2) 385 - 399, April 2016. https://doi.org/10.1215/17358787-3495693

Information

Received: 14 April 2015; Accepted: 11 July 2015; Published: April 2016
First available in Project Euclid: 4 April 2016

zbMATH: 1354.43003
MathSciNet: MR3481109
Digital Object Identifier: 10.1215/17358787-3495693

Subjects:
Primary: 43A25
Secondary: 22D15, 43A45

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.10 • No. 2 • April 2016
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