A Property of the Haar Measure of Some Special LCA Groups
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...
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| Format: | Article |
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| Language: | English |
| Published: |
University of Tehran
2006-09-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
| Online Access: | https://jsciences.ut.ac.ir/article_31764_7c0225f4f36a8d67fad6b6ae7135f6fb.pdf |
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| Summary: | 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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| ISSN: | 1016-1104 2345-6914 |