Pré-Publication, Document De Travail Année : 2020

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

Résumé

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, Luc\`a and Valeri (2018), who proved the result for integer values of the regularity parameter $s$.

Dates et versions

ensl-04829798 , version 1 (10-12-2024)

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Giuseppe Genovese, Renato Lucà, Nikolay Tzvetkov. Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS. 2024. ⟨ensl-04829798⟩
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