A construction of orthogonal compactly supported multiwavelets on \(\mathbf R^2\)
This paper provides the general construction of the continuous, orthogonal, compactly supported multiwavelets associated with a class of continuous, orthogonal, compactly supported scaling functions that contain piecewise linear functions on a uniform triangulation of \({\mathbb{R}}^2\). This class of scaling functions is a generalization of a set of scaling functions first constructed by \textit{J. S. Geronimo} and \textit{D. Hardin} [J. Math. Anal. Appl. 176, No. 2, 561-586 (1993; Zbl 0778.65009)] and \textit{G. C. Donovan, J. S. Geronimo} and \textit{D. P. Hardin} [SIAM J. Math. Anal. 27, No. 6, 1791-1815 (1996; Zbl 0857.42023)]. A specific set of scaling functions and associated multiwavelets with symmetry properties, is constructed.
scientific article; zbMATH DE number 1512545