On some extensions of the A-model

Opuscula Mathematica

article

Rytis Juršėnas¹ 

[1] Vilnius University, Institute of Theoretical Physics and Astronomy

关键词: 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.;   

DOI  :  10.7494/OpMath.2020.40.5.569

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

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.

【 授权许可】

CC BY-NC