Compact open spectral sets in Q(p)

Aihua Fan (1) , Shilei Fan , Ruxi Shi

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

In this article, we prove that a compact open set in the field Q(p) of p-adic numbers is a spectral set if and only if it tiles Q(p) by translation, and also if and only if it is p-homogeneous which is easy to check. We also characterize spectral sets in Z/p(n)Z (p >= 2 prime, n >= 1 integer) by tiling property and also by homogeneity. Moreover, we construct a class of singular spectral measures in Q(p), some of which are self similar measures. (C) 2016 Elsevier Inc. All rights reserved.

Domaines: Mathématiques [math]

Aihua Fan, Shilei Fan, Ruxi Shi. Compact open spectral sets in Q(p). Journal of Functional Analysis, 2016, 271 (12), pp.3628-3661. ⟨10.1016/j.jfa.2016.08.021⟩. ⟨hal-03622008⟩