Local Λ sets for profinite groups

Abstract

Preliminaries. Let G be a compact group with normalized Haar measure λβ. For p e [ l , [ the Banach space of pth power integrable complex-valued functions on G is denoted (L(G), || | |p). The dual object G of G is taken to be a maximal set of pairwise inequivalent continuous irreducible unitary representations of G. For each σeG let da be the degree or dimension of the representation space of σ and let Xσ denote its trace. The Fourier transform of / 6 L\G) is the matrix-valued function f on G defined by