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.