Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations - Hassi, Seppo; de Snoo, H.S.V.; Szafraniec, F.H. (Elsevier, 2012)
The notion of a maximally nondensely defined symmetric operator or relation is introduced and characterized. The selfadjoint extensions (including the generalized Friedrichs extension) of a class of maximally nondensely defined symmetric operators are described. The description is given by means of the theory of ordinary boundary triplets and exhibits the extensions as infinite-dimensional perturbations of a certain selfadjoint operator extension of the symmetric operator.
Keywords: Symmetric operator; Generalized Friedrichs extension; Weyl function; Boundary triplet; Graph perturbation; Matematiikka