Abstract
Hilbert spaces are defined, and the theory of Fourier series introduced. Group actions, unitary representations, the spectral theory of compact abelian groups, and the weight decomposition are introduced. Various notions of integration of functions taking values in a Banach space are introduced.
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Einsiedler, M., Ward, T. (2017). Hilbert Spaces, Fourier Series, and Unitary Representations. In: Functional Analysis, Spectral Theory, and Applications. Graduate Texts in Mathematics, vol 276. Springer, Cham. https://doi.org/10.1007/978-3-319-58540-6_3
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DOI: https://doi.org/10.1007/978-3-319-58540-6_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-58539-0
Online ISBN: 978-3-319-58540-6
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