Abstract
Spectral theory is developed in more general settings, including that of commuting normal operators. The measurable functional calculus is developed, and the spectral theorem for unitary representations of locally compact abelian groups is proved. This is used to show the full duality theory for locally compact abelian groups, including the Pontryagin isomorphism theorem.
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Einsiedler, M., Ward, T. (2017). Spectral Theory and Functional Calculus. 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_12
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DOI: https://doi.org/10.1007/978-3-319-58540-6_12
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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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