Groups with Atomic Regular Representation
A locally compact group G is called an [AR] group if the left regular representation of G is the direct sum of irreducible representations. A number of results related to the construction of [AR] groups and their properties are surveyed. The relevance of [AR] groups in the occurrence of nontrivial projections in L1(G) and in higher-dimensional continuous wavelet transforms is presented.
KeywordsIrreducible Representation Compact Group Banach Algebra Modular Function Regular Representation
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