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arXiv 2008.100012020-08-23math.PRmath.APmath.FA

Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS

Giuseppe Genovese, Renato Lucà, Nikolay Tzvetkov

英文摘要：

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 $s$.

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