On spectral Cantor measures

Abstract

A probability measure in ℝd is called a spectral measure if it has an orthonormal basis consisting of exponentials. In this paper, we study spectral Cantor measures. We establish a large class of such measures, and give a necessary and sufficient condition on the spectrum of a spectral Cantor measure. These results extend the studies by Jorgensen and Pedersen (J. Anal. Math. 75 (1998), 185-228) and Strichartz (J. D'Analyse Math. 81 (2000), 209-238). © 2002 Elsevier Science (USA).