Abstract
Let SG denote the Sierpinski gasket with Hausdorff measure μ of dimensionlog 3/log 2, let PLk denote the continuous piecewise linear functions with respect to the usual triangulation of SG into 3k triangles, and let Wk denote the orthogonal complement of PLk−1 in PLk. We construct a basis for each Wk, so that the entire collection is a frame for L2(dμ). This wavelet basis is obtained from three wavelet generators by scaling, translation and rotation, and the wavelets are supported either by one corner triangle or a pair of adjacent triangles in the triangulation of level k − 1. Analogous bases are constructed in the von Koch curve, the hexagasket, and the n-dimensional analog of SG.
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