On Spectral Cantor Measures

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. DʹAnalyse Math.81 (2000), 209–238).