Square Laplacian perturbed by inverse fourth-power potential. I Self-adjointness (real case)

The self-adjointness of Delta(2) + kappa vertical bar x vertical bar(-4) (kappa > kappa(0) = kappa(0)(N)) in L-2(R-N) is established as an application of the perturbation theorem in terms of Re(Au, B(epsilon)u), u is an element of D(A), for two non-negative self-adjoint operators A, B in a Hilbert space, where the family {B-epsilon}(epsilon>0) is the Yosida approximation of B. A key to the proof lies in a new inequality for the functions nu is an element of L-2(R-N) with vertical bar x vertical bar(2) Delta v is an element of L-2(R-N) derived by using two real parameters.