On some extensions of the A-model

• Main Author: Rytis Juršėnas
• Format: Article
• Language: English
• Published: AGH Univeristy of Science and Technology Press 2020-10-01
• Series: Opuscula Mathematica
• Subjects: 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
• Online Access: https://www.opuscula.agh.edu.pl/vol40/5/art/opuscula_math_4032.pdf
• ISSN: 1232-9274

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.