We consider a self-adjoint, purely absolutely continuous operator M⁠. Let P be a rank one
operator Pu=⟨ φ, u⟩ φ such that for β 0 H β 0≔ M+ β 0 P has a simple eigenvalue E 0 …

Consider a family of Sturm-Liouville operators H θ on the half-axis defined as H _ θ u=-u''+ q
(x) u 0\leqslant x< ∞ with the boundary condition u (0)\cos θ+ u'(0)\sin θ= 0 0\leqslant θ< π …

This is a discussion of some aspects of the relation between boundary conditions and
spectra of Sturm-Liouville operators. It is intended to review results which show how the …

“We consider a self-adjoint, purely absolutely continuous operator M. Let P be a rank-one
operator Pu=〈 ϕ, u〉 ϕ such that for β0, Hβ0:= M+ β0P has a simple eigenvalue E0 …