Eberlein convolution as an inner product and quantitative Bombieri--Taylor results

Abstract

We present a simple argument providing a very general Bombieri--Taylor-type result to compute Bragg peaks in diffraction theory as limits. At its abstract core the argument relies on considering the Eberlein convolution as an inner product. This inner product gives an abstract version of a Cauchy--Schwarz type inequality which implies the Bombieri--Taylor-type result as well as generalizations.