Functional model of a closed non-selfadjoint operator
In this paper, authors construct the symmetric functional model of an arbitrary closed operator with nonempty resolvent set acting on a separable Hilbert space. The construction is based on the explicit form of the Sz.-Nagy--Foiaş model of a closed dissipative operator, the Potapov--Ginzburg transform of characteristic functions, and certain resolvent identities. All considerations are carried out under minimal assumptions, and the obtained results are directly applicable to problems typically arising in mathematical physics. Also, explicit formulae for all the objects involved in the model construction are provided.
scientific article; zbMATH DE number 5294661