We introduce and study “norm-multiplicative” homomorphisms φ:L1(F)→Mr(G) between group measure algebras, φ:L1(ωF)→M(ωG) Beurling where F G are locally compact groups with continuous weights ωF ωG. Through a unified approach we recover, sometimes strengthen, many of the main known results concerning isomorphisms these (Beurling) algebras. provide first description all positive φ:L1(F)→Mr(G). sta...

Let Lω(G) be a Beurling algebra on a locally compact abelian group G. We look for general conditions on the weight which allows the vanishing of continuous derivations of Lω(G). This leads us to introducing vector-valued Beurling algebras and considering the translation of operators on them. This is then used to connect the augmentation ideal to the behavior of derivation space. We apply these ...

We investigate Beurling-Fourier algebras, a weighted version of Fourier on various Lie groups focusing their spectral analysis. will introduce refined general definition weights the dual locally compact and associated algebras. Constructions nontrivial be presented cases representative examples groups, namely SU(n), Heisenberg group H, reduced Hr, Euclidean motion E(2) its simply connected cove...