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arXiv · 2606.27008

Plancherel Identities for unbounded subsets of $\mathbb R^d$

Dorin Ervin Dutkay·Piyali Chakraborty
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Abstract

We present a class of pairs of subsets of $\mathbb R^d$ for which the Fourier transform, when restricted to these subsets, is an isometric isomorphism, and thus the Plancherel identity is satisfied. The sets are invariant under translations by dual full-rank lattices.

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Dorin Ervin Dutkay, Piyali Chakraborty. 2026-06-25. Plancherel Identities for unbounded subsets of $\mathbb R^d$. https://arxiv.org/abs/2606.27008

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