Local Wiener's Theorem and Coherent Sets of Frequencies

TL;DR

This paper introduces a local Wiener-Levin theorem analog to analyze measures with discrete support and spectrum, providing new criteria for identifying coherent frequency sets in Euclidean space.

Contribution

It develops a local Wiener-Levin theorem variant and establishes novel sufficient conditions for discrete sets to be coherent frequency sets.

Findings

Established a local Wiener-Levin theorem analog.

Derived new criteria for coherent frequency sets.

Enhanced understanding of measures with discrete support and spectrum.

Abstract

Using a local analog of the Wiener-Levi theorem, we investigate the class of measures on Euclidean space with discrete support and spectrum. Also, we find a new sufficient conditions for a discrete set in Euclidean space to be a coherent set of frequencies.