Spectral Measures on Locally Fields

2015/05/22 by Ai Hua Fan, Fan, Ai Hua
Mathematics · #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.FA

paper · pdf · doi:10.48550/arxiv.1505.06230

to be published in the preceedings of Conference: ICDEA 2014 - Difference Equations, Discrete Dynamical Systems and Applications, Springer

arxiv created 2015/05/22 · openalex publication_date 2015/05/22 · arxiv updated 2015/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Exact local distribution of the absolutely continuous spectral measure
• On p-adic spectral measures
• Spectral conditions for strong local nondeterminism and exact Hausdorff measure of ranges of Gaussian random fields
• Stability of Singular Spectral Types under Decaying Perturbations
• The continuity of Beurling density and Beurling dimension of spectra of a class of self-affine spectral measures