On semibounded canonical systems Original Research Article

We present two inverse spectral relations for canonical differential equations Jy′(x)=-zH(x)y(x), xset membership, variant[0,L): Denote by QH the Titchmarsh–Weyl coefficient associated with this equation. We show: If the Hamiltonian H is on some interval [0,epsilon (Porson)) of the formimagewith a nondecreasing function v, then limxsouth east arrow0v(x)=limy→+∞QH(iy). If H is of the above form on some interval [l,L), then limxNE pointing arrowLv(x)=limzNE pointing arrow0QH(z). In particular, these results are applicable to semibounded canonical systems, or canonical systems with a finite number of negative eigenvalues, respectively.