Abstract
We have seen explicit examples of square integrable representations in the last chapter, related to the SU(1, 1) and the connected affine groups. Here, we work out a few more examples to both illustrate the general theory of square integrable representations better and get a deeper understanding of the nature of the Duflo—Moore operator C, appearing in the orthogonality relations. We then move on to deriving a generalization of the notion of square integrability to accomodate CS of the Gilmore—Perelomov type and vector CS.
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© 2000 Springer Science+Business Media New York
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Ali, S.T., Antoine, JP., Gazeau, JP. (2000). Some Examples and Generalizations. In: Coherent States, Wavelets and Their Generalizations. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1258-4_9
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DOI: https://doi.org/10.1007/978-1-4612-1258-4_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7065-2
Online ISBN: 978-1-4612-1258-4
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