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arXiv · 2501.04349

Spectral synthesis in multidimensional Fourier algebras

Kanupriya·N. Shravan Kumar
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Abstract

Let $G$ be a locally compact group and let $A^n(G)$ denote the $n$-dimensional Fourier algebra, introduced by Todorov and Turowska. We investigate spectral synthesis properties of the multidimensional Fourier algebra $A^n(G).$ In particular, we prove versions of the subgroup lemma, injection, and inverse projection theorems for both spectral sets and Ditkin sets. Additionally, we provide a result on the parallel synthesis between $A^n(G)$ and $A^{n+1}(G)$ and finally prove Malliavin's theorem.

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BibTeXRIS

Kanupriya, N. Shravan Kumar. 2025-01-08. Spectral synthesis in multidimensional Fourier algebras. https://arxiv.org/abs/2501.04349

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