On square root domains for non-self-adjoint Sturm-Liouville operators - Nichols, R.; Hofmann, S.; Gesztesy, F. (Methods of Functional Analysis and Topology, 2013)
We determine square root domains for non-self-adjoint Sturm-Liouville operators of the type L_p,q,r,s = - ddxpddx+rddx-ddxs+q in L^2((c,d);dx), where either (c,d) coincides with the real line R, the half-line (a,∞), a R, or with the bounded interval (a,b) R, under very general conditions on the coefficients q, r, s. We treat Dirichlet and Neumann boundary conditions at a in the half-line case, and Dirichlet and/or Neumann boundary conditions at a,b in the final interval context. (In the particular case p=1 a.e. on (a,b), we treat all separated boundary conditions at a, b.)