Related papers: On the structure of Spectral Sets

Recently we introduced the concept of localisability of ideals in the Fourier algebra of locally compact Abelian groups. It turns out that localisability can be used to characterise synthesisability of varieties. Based on this we show that…

For a locally compact group $G$, let $A^n(G)$ denote the multidimensional Fourier algebra given by $ \otimes_{n}^{eh} A(G).$ This work explores the approximation identity and operator amenability of the algebra $A^n(G)$. Further, we study…

For a locally compact group $G$, let $A(G)$ denote its Fourier algebra and $\hat{G}$ its dual object, i.e. the collection of equivalence classes of unitary represenations of $G$. We show that the amenability constant of $A(G)$ is less than…

Let $G$ be a locally compact group. We show how complemented ideals in the Fourier algebra $A(G)$ of $G$ arise naturally from a class of thin sets known as Leinert sets. Moreover, we also present an explicit example of a closed ideal in…

We give for a compact group G, a full characterisation of when its Fourier algebra A(G) is weakly amenable: when the connected component of the identity G_e is abelian. This condition is also equivalent to the hyper-Tauberian property for…

In this paper we solve a long-standing problem which goes back to Laurent Schwartz's work on mean periodic functions. Namely, we completely characterise those locally compact Abelian groups having spectral synthesis. So far a…

These notes briefly discuss basic notions concerning locally compact abelian topological groups and Fourier transforms of functions on them.

We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier-Baranov Theorem. As…

We establish the spectral gap property for dense subgroups generated by algebraic elements in any compact simple Lie group, generalizing earlier results of Bourgain and Gamburd for unitary groups.

Given a free action of a compact Lie group $G$ on a unital C*-algebra $\mathcal{A}$ and a spectral triple on the corresponding fixed point algebra $\mathcal{A}^G$, we present a systematic and in-depth construction of a spectral triple on…

We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…

In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…

We discuss some notions of compactness and convergence relative to a specified family F of subsets of some topological space X. The two most interesting particular cases of our construction appear to be the following ones. (1) The case in…

In this paper, we develop a new approach that allows to identify the Gelfand spectrum of weighted Fourier algebras as a subset of an abstract complexification of the corresponding group for a wide class of groups and weights. This…

Let $G$ be a finite abelian group and $A$ a subset of $G$. The spectrum of $A$ is the set of its large Fourier coefficients. Known combinatorial results on the structure of spectrum, such as Chang's theorem, become trivial in the regime…

In this paper we will study the homological properties of various natural modules associated to the Fourier algebra of a locally compact group. In particular, we will focus on the question of identifying when such modules will be projective…

We locate the complexity of the set of closed sets of uniqueness U(G), for G locally compact Lie group and of the set of closed sets of extended uniqueness U_0(G), for G connected abelian Lie group. More concretely, we prove that with…

We obtain a set of generalized eigenvectors that provides a generalized spectral decomposition for a given unitary representation of a commutative, locally compact topological group. These generalized eigenvectors are functionals belonging…

In his classical paper, Laurent Schwartz proved that on the real line, in every linear translation invariant space of continuous complex valued functions, which is closed under compact convergence the exponential monomials span a dense…

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…