Abstract
The spectral theory of unitary operators is introduced, and Herglotz’ theorem for positive-definite sequences proved. The main properties of spectral measures for unitary operators are described, and an application to the joining theory of measure-preserving dynamical systems is given. Fourier theory and the Fourier transform are developed further, and a form of uncertainty principle is given.
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Einsiedler, M., Ward, T. (2017). Unitary Operators and Flows, Fourier Transform. 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_9
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DOI: https://doi.org/10.1007/978-3-319-58540-6_9
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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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