is a spectral pair if and only if is a tiling pair with. . For any invertible linear transformation ,The equivalent property of spectral pair 、tiling pair is hold. The fact has been proved by Lagarias、Reeds and Wang with density method . In this article author presents another approach to prove it, use the technique of approximating identity from the corresponding inequality.
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杜娟. 线性变换下的谱与Tiling的一些性质[J]. 科学技术与工程, 2010, (26): . dujuan. On a characterization of Linear transform spectra and tiling[J]. Science Technology and Engineering,2010,(26).