Hill's spectral curves and the invariant measure of the periodic KdV equation (Q316703)

The paper investigates the periodic spectrum of Hill's equation \(-f''+q(x)f=\lambda f\) with \(x\in\mathbb R\), where \(q\) is \(2\pi\)-periodic with \(q\in L^2([0,2\pi])\). Several topics are discussed, including concentration and transportation of measures, fluctuations and sampling of periodic eigenvalues, linear statistics and sampling from the Paley-Wiener space.