A Property of the Haar Measure of Some Special LCA Groups
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The Euclidean group (Rn,+) where (n?N, plays a key role in harmonic analysis. If we consider the Lebesgue measure ()nd?xR as the Haar measure of this group then 12(2)()nd?x=d?RR. In this article we look for LCA groups K, whose Haar measures have a similar property. In fact we will show that for some LCA groups K with the Haar measure K?, there exists a constant such that 0KC>()(2)KKK?A=C?A for every measurable subset A of K. Moreover we will characterize this constant for some special groups.
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Journal title
volume 17 issue 3
pages -
publication date 2006-09-01
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