Abstract
In the present chapter, we initiate our study of harmonic analysis proper. The basic operation in harmonic analysis is convolution; in §99, 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.
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© 1979 Springer-Verlag New York, Inc.
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Hewitt, E., Ross, K.A. (1979). Convolutions and group representations. In: Abstract Harmonic Analysis. Grundlehren der mathematischen Wissenschaften, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8638-2_5
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DOI: https://doi.org/10.1007/978-1-4419-8638-2_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94190-5
Online ISBN: 978-1-4419-8638-2
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