Abstract
We showed in Chap. VIII, n° 15 that the function 1/ ch π x is equal to its Fourier transform. A change of variable then shows that, for all t > 0, the Fourier transform of \(x \longmapsto 1/ \ {\rm{ch}}({\pi}{x}/t)\) is \(x \longmapsto t/ \ {\rm{ch}}({\pi}{x}t)\).
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Godement, R. (2015). The series \(\sum 1/ {\rm{cos}} \ \pi n z\; {\rm{and}}\; \sum {\rm{exp}} \left(\pi in^2z\right)\) . In: Analysis IV. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-16907-1_10
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DOI: https://doi.org/10.1007/978-3-319-16907-1_10
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16906-4
Online ISBN: 978-3-319-16907-1
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