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 $P_{n+1}^{\pm }\subseteq P_n^{\pm }$, nontrivial extensions in the A-model are constructed for the symmetric restrictions in the subspaces.

to appear in Opuscula Mathematica