1 Elementary Results -- 2 An Approximation Theorem for CV2(G) -- 3 The Figa-Talamanca Herz Algebra -- 4 The Dual of Ap(G) -- 5 CVp(G) as a Module on Ap(G) -- 6 The Support of a Convolution Operator -- 7 Convolution Operators Supported by Subgroups -- 8 CVp(G) as a Subspace of CV2(G).

This volume is devoted to a systematic study of the Banach algebra of the convolution operators of a locally compact group. Inspired by classical Fourier analysis we consider operators on Lp spaces, arriving at a description of these operators and Lp versions of the theorems of Wiener and Kaplansky-Helson.