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?
2026-04-07 21:17:05.1775596625
Higher Dimensional Paley Wiener Theorem
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Reed/Simon, Functional analysis, chapter IX, Theorem IX.11. It can also be found somewhere in Rudin's book.