On the orthogonality of measures of different spectral type with respect to twisted Eberlein convolution

Abstract

In this paper we show that under suitable conditions on their Fourier--Bohr coefficients, the twisted Eberlein convolution of a measure with pure point diffraction spectra and a measure with continuous diffraction spectra is zero. In particular, the diffraction spectrum of a linear combinations of the two measures is simply the linear combinations of the two diffraction spectra with absolute value square coefficients.

24 pages, updated using the twisted version of the Eberlein convolution