Construction of compactly supported refinable componentwise polynomial functions in \(\mathbb R^2\)
A compactly supported function \(f:\,{\mathbb R}^2 \to {\mathbb C}\) is called a componentwise polynomial, if there exists an open set \(G\subset {\mathbb R}^2\) such that \({\mathbb R}^2 \setminus G\) is a set of measure zero and the restriction of \(f\) on any connected open component of \(G\) coincides with some polynomial. Let \(f\in L^1({\mathbb R}^2)\) be a compactly supported function satisfying a refinement equation with a diagonal dilation matrix. The authors give sufficient conditions for the mask symbol of \(f\) such that \(f\) is a componentwise polynomial. The componentwise polynomial is iteratively computed. Examples are presented too.
scientific article; zbMATH DE number 5997785
scientific article