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Plancherel's theorem is explored in detail, showcasing its role in generalizing the completeness of Fourier series. The book delves into non-commutative harmonic analysis, beginning with matrix group analysis, Lie algebras, and the classification of SU(2) representations. It presents the Peter-Weyl theorem, which extends Fourier series completeness to compact non-commutative groups, and examines the Heisenberg group, illustrating how the regular representation decomposes as a direct integral. Acknowledgments highlight contributions from various scholars.
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A First Course in Harmonic Analysis, Anton Deitmar
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- Année de publication
- 2005
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