Spectral Measures Generated By Arbitrary And Random Convolutions

Keywords

Infinite convolution; Self-affine; Spectral measure; Tile

Abstract

We study spectral measures generated by infinite convolution products of discrete measures generated by Hadamard triples, and we present sufficient conditions for the measures to be spectral, generalizing a criterion by Strichartz. We then study the spectral measures generated by random convolutions of finite atomic measures and rescaling, where the digits are chosen from a finite collection of digit sets. We show that in dimension one, or in higher dimensions under certain conditions, “almost all” such measures generate spectral measures, or, in the case of complete digit sets, translational tiles. Our proofs are based on the study of self-affine spectral measures and tiles generated by Hadamard triples in quasi-product form.

Publication Date

2-1-2017

Publication Title

Journal des Mathematiques Pures et Appliquees

Volume

107

Issue

2

Number of Pages

183-204

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.matpur.2016.06.003

Socpus ID

84997456809 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84997456809

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