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

2020/08/23 by Giuseppe Genovese, Renato Lucà, Genovese, Giuseppe +3 · 1 citation
Mathematics · Physics and Astronomy · #35Q55 #37A05 #60G22 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Quantum Chromodynamics and Particle Interactions

paper · pdf · doi:10.48550/arxiv.2008.10001

openalex publication_date 2020/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The periodic DNLS gauge is an anticipative map with singular generator which\nrevealed crucial in the study of the periodic derivative NLS. We prove\nquasi-invariance of the Gaussian measure on L²( T) with covariance\n[1+(- D)^s]^-1 under these transformations for any s> frac12. This\nextends previous achievements by Nahmod, Ray-Bellet, Sheffield and Staffilani\n(2011) and Genovese, Luc `a and Valeri (2018), who proved the result for\ninteger values of the regularity parameter s.\n

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