Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smooth and weak synthesis of the anti-diagonal in Fourier algebras of
  Lie groups   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
$\check{\Delta}_G=\{(g,g^{-1})\in G\times G \mid g\in G\}$ is both a set of
local smooth synthesis and a set of local weak synthesis of degree at most
$[\frac{n}{2}]+1$ for $A(G\times G)$. We achieve this by using the concept of
the cone property in \cite{ludwig-turowska}. For compact $G$, we give an
alternative approach to demonstrate the preceding results by applying the ideas
developed in \cite{forrest-samei-spronk}. We also present similar results for
sets of the form $HK$, where both $H$ and $K$ are subgroups of $G\times G\times
G\times G$ of diagonal forms. Our results very much depend on both the
geometric and the algebraic structure of these sets.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph