On the symplectic phase space of KdV

Details On the symplectic phase space of KdV On the symplectic phase space of KdV

2007-10-06

arxiv.org/abs/0710.1381v1

Mathematics

Functional Analysis

Scientific paper

We prove that the Birkhoff map $\Om$ for KdV constructed on $H^{-1}_0(\T)$ can be interpolated between $H^{-1}_0(\T)$ and $L^2_0(\T)$. In particular, the symplectic phase space $H^{1/2}_0(\T)$ can be described in terms of Birkhoff coordinates. As an application, we characterize the regularity of a potential $q\in H^{-1}(\T)$ in terms of the decay of the gap lengths of the periodic spectrum of Hill's operator on the interval $[0,2]$.

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