2025/01/08 by Kanupriya, Kumar, N. Shravan
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2501.04349
Let G be a locally compact group and let An(G) denote the n-dimensional Fourier algebra, introduced by Todorov and Turowska. We investigate spectral synthesis properties of the multidimensional Fourier algebra An(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 An(G) and An+1(G) and finally prove Malliavin's theorem.