On the spectrum of the Lax operator of the Benjamin-Ono equation on the torus

Abstract We investigate the spectrum of the Lax operator L u of the Benjamin-Ono equation on the torus for complex valued potentials u in the Sobolev space H − s ( T , C ) , 0 ≤ s 1 / 2 , with small imaginary part and prove analytic properties of the moment map, defined in terms of spectral data of L u .