Opuscula Math. 40, no. 5 (2020), 569-597
https://doi.org/10.7494/OpMath.2020.40.5.569

Opuscula Mathematica

# On some extensions of the A-model

Rytis Juršėnas

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.

Mathematics Subject Classification: 47A56, 47B25, 47B50, 35P05.

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• Communicated by Aurelian Gheondea.
• Revised: 2020-05-12.
• Accepted: 2020-07-30.
• Published online: 2020-10-10.