Analysis Seminar

Zhihao Zhang, University of Waterloo

Spectra of Beurling Algebras of Discrete Abelian Groups

We will discuss a variant of the group algebra, called the Beurling algebra. These algebras differ from their classical counterpart through the addition of a weight function modifying the norm. The Gelfand spectrum of the group algebra of absolutely integrable functions on an abelian group, G, is well known to be the Pontryagin dual of G. In the case of a Beurling algebra, the Gelfand spectrum can be much larger for suitable weights. We will focus on the Beurling algebra of a discrete abelian group, G, and give a description of its Gelfand spectrum in terms of a seminorm constructed from a symmetric weight.

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