Symmetric extensions of symmetric linear relations (operators) preserving the multivalued part - Mogilevskii, V. I. (Methods of Functional Analysis and Topology, 2018)
Let H be a Hilbert space and let A be a symmetric linear relation (in particular, a nondensely defined operator) in H. By using the concept of a boundary triplet for A^* we characterize symmetric extensions AA preserving the multivalued part of A. Such a characterization is given in terms of an abstract boundary parameter and the Weyl function of the boundary triplet. Application of these results to the Hamiltonian system Jy’-B(t)y=λΔ(t) y enabled us to describe its matrix solutions generating the generalized Fourier transform with the nonempty set of respective spectral functions.