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Mar 11, 2022 at 22:11 comment added paul garrett Yes, the strong form of Paley-Wiener theorems (stronger than the original more $L^2$-oriented version of Paley and Wiener from 1934) is exactly the point. Yes, it is slightly peculiar that functionals on compactly-supported functions on the real line might be evaluation of the analytic continuations of their Fourier transforms off the real line. But it is so. :)
S Jan 12, 2014 at 8:24 review Late answers
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S Jan 12, 2014 at 8:24 review First posts
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Jan 12, 2014 at 8:19 history edited 7891user CC BY-SA 3.0
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Jan 12, 2014 at 8:07 history answered 7891user CC BY-SA 3.0