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• W1987200196 abstract "Avila and Jitomirskaya prove that the spectral measure $mu_{lambda v, alpha,x}^f$ of quasi-periodic Schr{o}dinger operator is $1/2$-H{o}lder continuous with appropriate initial vector $f$, if $alpha $ satisfies Diophantine condition and $lambda$ is small. In the present paper, the conclusion is extended to that for all $alpha$ with $beta(alpha)<infty$, the spectral measure $mu_{lambda v, alpha,x}^f$ is $1/2$-H{o}lder continuous with small $lambda$, if $v$ is real analytic in a neighbor of ${|Im x|leq Cbeta}$, where $C$ is a large absolute constant. In particular, the spectral measure $mu_{lambda, alpha,x}^f$ of almost Mathieu operator is $1/2$-H{o}lder continuous if $|lambda|<e^{-Cbeta}$ with $C$ a large absolute constant." @default.
• W1987200196 created "2016-06-24" @default.
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• W1987200196 date "2015-01-01" @default.
• W1987200196 modified "2023-10-16" @default.
• W1987200196 title "Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime" @default.
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• W1987200196 doi "https://doi.org/10.1063/1.4904835" @default.
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