Abstract
As we have shown in Section 2.2.8, irreducible finite dimensional representations of commutative groups are one-dimensional. In particular, irreducible representations of the additive group R are onedimensional. In order to find them it is necessary to solve the functional equation f(t + s) = f(t) f (s), where f is a scalar function. It follows from formula (4) of Section 2.1.5 that f’(t) = f’(0) f (t).
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© 1991 Springer Science+Business Media Dordrecht
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Vilenkin, N.J., Klimyk, A.U. (1991). Commutative Groups and Elementary Functions. The Group of Linear Transformations of the Straight Line and the Gamma-Function. Hypergeometric Functions. In: Representation of Lie Groups and Special Functions. Mathematics and Its Applications (Soviet Series), vol 72. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3538-2_4
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DOI: https://doi.org/10.1007/978-94-011-3538-2_4
Publisher Name: Springer, Dordrecht
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