Abstract
This paper presents a self contained approach to the theory of convolution operators on locally compact groups (both commutative and non commutative) based on the use of the Figà–Talamanca Herz algebras. The case of finite groups is also considered.
Highlights
A p-convolution operator T on a locally compact group G is a continuous linear operator of Lp (G)such that T commutes with left translations
Every bounded function on a LCA can be recovered from his spectrum (Corollary 4)
We present a generalization of the first part of Theorem 6, to every 1 < p < ∞ and to every locally compact group
Summary
A p-convolution operator T on a locally compact group G is a continuous linear operator of Lp (G)such that T commutes with left translations. Observe that for G, an arbitrary locally compact group, CVp (G) with the composition of operators, as a product, is a unital Banach algebra: Let G be a locally compact abelian group, 1 < p < ∞ and T ∈ CVp (G).
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