01-189 Qing-Hui LIU, Bo TAN, Zhi-Xiong WEN, Jun WU

Measure Zero Spectrum of a class of Schr\"odinger operators (261K, Postscript, 259k) May 21, 01

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Abstract. We study the measure of the spectrum of a class of one-dimensional discrete Schr\"odinger operators $H_{v,\omega}$ with quasi-periodic potential $v(\omega)$ generated by any primitive substitution. It is known that the spectrum of $H_{v,\omega}$ is singular continuous (\cite{HKS}). We will give a more exact result that the spectrum of $H_{v,\omega}$ is a Cantor set of Lebesgue measure zero.

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