Biorthogonal two-direction refinable function and two-direction wavelet
The author generalizes the theory of refinable functions and biorthogonal wavelets. He considers a so-called two-direction refinable function \(\varphi \in L^2({\mathbb R})\) which satisfies \[ \varphi(x)=\sum_{k=-\infty}^{\infty}\big(p_k^{+}\, \varphi(2x-k) + p_k^{-}\,\varphi(k-2x)\big) \] with 2 masks \(\{p_k^{\pm}\}\in l^2({\mathbb Z})\). The properties of the positive/negative-direction symbols are studied. Using these symbols, biorthogonal two-direction refinable functions and corresponding biorthogonal two-direction wavelets are characterized. Finally, two examples illustrate the construction of biorthogonal two-direction wavelets.
scientific article; zbMATH DE number 5115442
scientific article