Matt Mazowita, Department of Mathematical and Statistical Sciences, University of Alberta
“From Group to Beurling Algebras”
One of the most important Banach algebras in abstract harmonic analysis is the group algebra of a locally compact group, which consists of functions which are integrable (against Haar measure) with the convolution product. If instead we ask that the functions are integrable when multiplied by a weight function we obtain the Beurling (or weighted convolution) algebra. There are also weighted analogues of many other related objects. For a large class of weights, results for group algebras can be extended to the corresponding Beurling algebras. I will present some such results concerning amenability, isometric isomorphisms, the extension of the product on the Banach algebra to its second dual space, and the existence of finite sets which determine some algebraic and topological properties.