2008/09/16 by B. Doug Park, Park, B. Doug, Ebrahim Samei +1 · 1 citation
Mathematics · #43A30 #43A45 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Group Theory (math.GR) #math.FA #math.GR #msc:43A30 #msc:43A45
paper · pdf · doi:10.48550/arxiv.0809.2806
arxiv created 2008/09/16 · openalex publication_date 2008/09/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a Lie group of dimension n, and let A(G) be the Fourier algebra of G. We show that the anti-diagonal \checkΔG=\(g,g-1)∈ G× G | g∈ G\ is both a set of local smooth synthesis and a set of local weak synthesis of degree at most [(n)/(2)]+1 for A(G× G). We achieve this by using the concept of the cone property in \citeludwig-turowska. For compact G, we give an alternative approach to demonstrate the preceding results by applying the ideas developed in \citeforrest-samei-spronk. We also present similar results for sets of the form HK, where both H and K are subgroups of G× G× G× G of diagonal forms. Our results very much depend on both the geometric and the algebraic structure of these sets.