标题： 多维傅里叶代数中的谱合成 显示英文标题

标题： Spectral synthesis in multidimensional Fourier algebras

摘要： 设$G$是一个局部紧致群，令$A^n(G)$表示由 Todorov 和 Turowska 引入的$n$维傅里叶代数。我们研究多维傅里叶代数$A^n(G).$的谱合成性质。特别是，我们证明了子群引理、注入和逆投影定理在谱集和 Ditkin 集上的版本。此外，我们提供了一个关于$A^n(G)$与$A^{n+1}(G)$之间的并行合成的结果，并最终证明了 Malliavin 定理。 显示英文摘要

摘要： 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.