论文标题
立方NLS运输的高斯措施的准不变，并在$ \ mathbf {t} $上进行三阶分散。
Quasi-Invariance of Gaussian Measures Transported by the Cubic NLS with Third-Order Dispersion on $\mathbf{T}$
论文作者
论文摘要
我们考虑了非线性schrödinger（nls）方程，并证明具有协方差的高斯度量$（1- \ partial_x^2）^{ - α} $ on $ l^2（\ mathbf t）$ is quasi-Invariant用于$α> 1/2 $的相关流量。这是敏锐的，并改善了以前在\ cite {ott}中获得的结果，其中获得了$α> 3/4 $的值。同样，我们的方法是完全不同的，更简单的，它基于radon-nikodym衍生物的显式公式。我们以与\ cite {cruz1}和\ cite {cruz2}相同的精神获得了后者的明确公式。这些论点是一般的，可以用于其他汉密尔顿方程。
We consider the Nonlinear Schrödinger (NLS) equation and prove that the Gaussian measure with covariance $(1-\partial_x^2)^{-α}$ on $L^2(\mathbf T)$ is quasi-invariant for the associated flow for $α>1/2$. This is sharp and improves a previous result obtained in \cite{OTT} where the values $α>3/4$ were obtained. Also, our method is completely different and simpler, it is based on an explicit formula for the Radon-Nikodym derivative. We obtain an explicit formula for this latter in the same spirit as in \cite{Cruz1} and \cite{Cruz2}. The arguments are general and can be used to other Hamiltonian equations.
