On a Criterion of Strichartz for Spectral Pairs

摘要

The author considers the spectrality of self-affine measures associated with a contractive iterated function system and an expansive iterated function system. Under the condition of a compatible pair, some necessary and sufficient conditions are determined respectively for a given pair to be a spectral pair. First, several equivalent forms of a criterion of Strichartz for spectral pairs are obtained. Then two necessary conditions for the same spectral pair are obtained. Finally, a detailed and rigorous proof of this criterion is provided.