Homogeneous approximation property for various directions

Abstract

In the theory of signal reconstruction, the homogeneous approximation property (HAP) for wavelets is useful. In this paper, we consider the HAP for the continuous wavelet transform with matrix dilation. When the dilation of wavelet is different in various directions, we show that the HAP holds in L2(Rd). The HAP also holds in L∞(Rd) when we add some conditions.