Singular Perturbations of Self-Adjoint Operators Associated with Rigged Hilbert Spaces
Let A be an unbounded self-adjoint operator in a Hilbert separable space \(H_0\) with rigging \(H_ - H_0 H_ +\) such that \(D(A) = H_ +\) in the graph norm (here, \(D(A)\) is the domain of definition of A). Assume that \(H_ +\) is decomposed into the orthogonal sum \(H_ + = M N_ +\) so that the subspace \(M_ +\) is dense in \(H_0\). We construct and study a singularly perturbed operator A associated with a new rigging \(H_ - H_0 0.5em H _ +\), where \(0.5em H _ + = M_ + = D(0.5em A )\), and establish the relationship between the operators A and A., number=5, journal=Ukrains’kyi Matematychnyi Zhurnal, author=Bozhok, R. V. and Koshmanenko, V. D., year=2005, month=May, pages=622–632