A probability measure in R 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 [9] and Strichartz [20].

In this paper, we study the confounder detection problem in the linear model, where the target variable Y is predicted using its n potential causes Xn = (x1, ..., xn) T . Based on an assumption of rotation invariant generating process of the model, recent study shows that the spectral measure induced by the regression coefficient vector with respect to the covariance matrix of Xn is close to a ...