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Is there a natural generalization of the Paley Wiener theorem to higher dimensions (i.e. relating a function $f \in L^2(K), K \subset \mathbb{R}^d$ compact, to an entire function in $\mathbb{C}^d$)? If so, where can I find a statement/proof of such a theorem?

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Reed/Simon, Functional analysis, chapter IX, Theorem IX.11. It can also be found somewhere in Rudin's book.

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  • $\begingroup$ perfect, thanks! $\endgroup$
    – mck
    Dec 23 '13 at 1:43
  • $\begingroup$ you are welcome $\endgroup$ Dec 23 '13 at 13:08

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