A note on measures whose diffraction is concentrated on a single sphere

TL;DR

This paper constructs a translation-bounded measure with spherically symmetric diffraction concentrated on a single sphere, answering a question posed by Strungaru.

Contribution

It provides a constructive example of such a measure, advancing understanding of diffraction measures in mathematical analysis.

Findings

Constructed a translation-bounded measure with specific diffraction properties.

Confirmed the existence of measures with diffraction concentrated on a single sphere.

Answered an open question in the field of diffraction measures.

Abstract

Is there a translation-bounded measure whose diffraction is spherically symmetric and concentrated on a single sphere? This note constructively answers this question of Strungaru in the affirmative.