Rajchman Algebras of Local Fields
The OGMC is a student-run conference which in which Ontario-based mathematics students present about their various research projects. This talk covered the second major research project of my PhD thesis. It provides a brief introduction to the Fourier algebra \(A(G)\) of a locally compact group \(G\), and examines a specific example of the \(p\)-adic group \(G = \mathbb{Q}_p^2 \rtimes \mathbb{O}_p^*\).
Given a locally compact group \(G\), the Rajchman algebra \(B_0(G)\) consists of matrix coefficients which vanish at infinity. This will necessarily contain the Fourier algebra \(A(G)\), though it may be strictly larger. In this talk, we introduce a class of groups derived from local fields, and investigate the relationship between \(A(G)\) and \(B_0(G)\).