Characterization of Riesz scaling functions in asimple case and orthonormal scaling functions of length not greater than 5

Abstract

Characterization of Riesz scaling functions and orthonormal scaling functions in certain simple cases is given. For example, a function $Φ with \widehat{\phi}= χ_{[a,b)}$ is a Riesz scaling function if and only if the point (a,b) belongs to a certain triangular region. We also characterize the orthonormal scaling functions with support [0,3] and [0,5] by means of Lawton matrix.