Self-adjoint extensions by additive perturbations

摘要: Let AN be the symmetric operator given by restriction of A to N , where is a self-adjoint on Hilbert space H and linear dense set which closed with respect graph norm D(A), domain A. We show that any extension Aof such D(A� )∩ D(A) = can additively decomposed sum A� ¯ A+T� both operators Ttake values in strong dual D(A). The whole whereas Tis explicitly written terms (abstract) boundary condition depending parameter � ,a an auxiliary isomorphic (as set) deficiency spaces . explicit connection Kre˘in's resolvent formula von Neumann's theory extensions given.