Convolutions and group representations
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In the present chapter, we initiate our study of harmonic analysis proper. The basic operation in harmonic analysis is convolution; in §19, we give a reasonably general definition of convolutions and develop with some care the fundamental properties of convolutions of measures. In §20, we examine explicit formulas for convolutions of measures and functions. In §21, we present some facts about representations of groups and algebras. In §22, we prove the existence of irreducible representations of locally compact groups.
KeywordsUnitary Representation Haar Measure Representation Versus Compact Abelian Group Cyclic Vector
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