On some extensions of the A-model

Abstract

The A-model for finite rank singular perturbations of class \(\mathfrak{H}_{-m-2}\setminus\mathfrak{H}_{-m-1}\), \(m \in \mathbb{N}\), is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces \((\mathfrak{H}_n)_{n\in\mathbb{Z}}\) admit an orthogonal decomposition \(\mathfrak{H}^-_n \oplus \mathfrak{H}^+_n\), with the corresponding projections satisfying \(P^{\pm}_{n+1}\subseteq P^{\pm}_n\), nontrivial extensions in the A-model are constructed for the symmetric restrictions in the subspaces.

Keywords

• finite rank higher order singular perturbation
• cascade (a) model
• peak model
• hilbert space
• scale of hilbert spaces
• pontryagin space
• ordinary boundary triple
• krein \(q\)-function
• weyl function
• gamma field
• symmetric operator
• proper extension
• resolvent