Parameterization of bivariate nonseparable orthogonal symmetric scaling functions with short support. (English) Zbl 1240.42121
Summary: Let \(I\) be a \(2 \times 2\) identity matrix, and \(M\) be a \(2\times 2\) dilation matrix with \(M^2 = 2I\). First, we present the correlation of the scaling functions with dilation matrix \(M\) and \(2I\). Then by relating the properties of scaling functions with dilation matrix \(2I\) to the properties of scaling functions with dilation matrix \(M\), we give a parameterization of a class of bivariate nonseparable orthogonal symmetric compactly supported scaling functions with dilation matrix \(M\). Finally, a construction example of nonseparable orthogonal symmetric and compactly supported scaling functions is given.
MSC:
42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |