Characterization of Riesz scaling functions in asimple case and orthonormal scaling functions of length not greater than 5간단한 경우의 Riesz 스케일링 함수와 길이가 5이하인 직교 스케일링 함수의 분류
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.