In this paper, we shall investigate the symmetry property of a multivariate orthogonal M -refinable function with a general dilation matrix M . For an orthogonal M -refinable function φ such that φ is symmetric about a point (centro-symmetric) and φ provides approximation order k, we show that φ must be an orthogonal M -refinable function that generates a generalized coiflet of order k. Next, w...

For a positive definite infinite matrix A, we study the relationship between its associated sequence of orthonormal polynomials and the asymptotic behaviour of the smallest eigenvalue of its truncation An of size n×n. For the particular case of A being a Hankel or a Hankel block matrix, our results lead to a characterization of positive measures with finite index of determinacy and of completel...