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

2021/11/03 by Nicolae Strungaru, Strungaru, Nicolae
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2111.02547

openalex publication_date 2021/11/03 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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.

Related

• Diffraction as a unitary representation and the orthogonality of measures with respect to the reflected Eberlein convolution
• The (twisted) Eberlein convolution of measures
• Twice Fourier transformable measures and diffraction theory
• Circles in diffraction
• Obtaining the Fourier spectrum via Fourier coefficients