A note on the linear independence of characteristic functions of self-similar sets

摘要

1. Introduction. In recent studies, it has turned out that there are interesting relations between self-similar lattice tiling and the construction of wavelets, see e.g. [8]. Let M be an expanding scaling matrix, i.e., M has integer entries and all its eigenvalues have modulus strictly larger than one. Then a set Q c 1R" gives rise to a self-similar tiling with respect to M if it satisfies.