Spectral Measures on Locally Fields

TL;DR

This paper investigates spectral measures on local fields, presenting foundational results such as stability, density theorems, spectral measure types, and properties of Radon-Nikodym derivatives.

Contribution

It introduces new results on spectral measures in local fields, including stability under perturbation and density properties, expanding the theoretical framework.

Findings

Stability of Bessel sequences under perturbation

Landau theorem on Beurling density for spectral measures

Law of pure type of spectral measures

Abstract

In this paper, we propose to study spectral measures on local fields. Some basic results are presented, including the stability of Bessel sequences under perturbation, the Landau theorem on Beurling density, the law of pure type of spectral measures, the boundedness of the Radon-Nikodym derivative of absolutely continuous $F$-spectral measures etc.