Observability of dispersive equations from line segments on the torus (Q6569369)

Let \(\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z}\). This paper considers the dispersive equation on \(\mathbb{T}\) \N\[\N\partial_tu=iP(D)u,\quad u(0,x)=u_0(x)\in L^2(\mathbb{T}),\N\]\Nwhere \(u=u(t,x)\) is a real or complex-valued function and \(P(D)\) is a Fourier multiplier operator with \(D= i^{- 1}\partial _x.\) The main result is Theorems 1.5 concerning observability of the dispersive equation from \(n = 2\) line segments.