Spectral structure and spectral eigenvalue problems of a class of self-similar spectral measures

摘要

Let mu be a probability measure with compact support in R. The measure mu, is called a spectral measure if there exists a countable set Lambda subset of R, called a spectrum of mu, such that the family of exponential functions {e(-2 pi i lambda x) : lambda is an element of Lambda} forms an orthonormal basis for L-2 (mu). In this paper we study the structure of spectra and the real number t such that both Lambda and t Lambda are spectra for a class of self-similar spectral measures, which have symmetric spectra. Some examples are given to explain our theory. (C) 2019 Elsevier Inc. All rights reserved.