论文标题
在周期性衍生NLS的仪表图下，低规律性高斯措施的准不变性
Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
论文作者
论文摘要
周期性DNLS仪表是一个带有单数发生器的预期图，揭示了对周期衍生物NLS的研究至关重要。我们证明了与任何$ s> \ frac12 $的这些转换下，我们证明了$ l^2（\ t）$在$ l^2（\ t）$上对高斯度量的准反变性。这扩展了Nahmod，Ray-Bellet，Sheffield和Staffilani（2011）以及Genovese，Lucà和Valeri（2018）的先前成就，后者证明了规律性参数$ S $的整数值的结果。
The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian measure on $L^2(\T)$ with covariance $[1+(-\D)^{s}]^{-1}$ under these transformations for any $s>\frac12$. This extends previous achievements by Nahmod, Ray-Bellet, Sheffield and Staffilani (2011) and Genovese, Lucà and Valeri (2018), who proved the result for integer values of the regularity parameter $s$.
