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On some extensions of the a-model

Jursenas Rytis

Opuscula Mathematica

2020

Vol. 40, no. 5

569--597

The A-model for finite rank singular perturbations of class [formula], is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces [formula] admit an orthogonal decomposition [formula], with the corresponding projections satisfying [formula], nontrivial extensions in the A-model are constructed for the symmetric restrictions in the subspaces.

Operators in divergence form and their Friedrichs and Krein extensions

Arlinskii Y., Kovalev Y.

Opuscula Mathematica

2011

Vol. 31, no. 4

501-517

For a densely defined nonnegative symmetric operator A = L*(2)L1 in a Hilbert space, constructed from a pair L1 ⊂ L2 of closed operators, we give expressions for the Friedrichs and Krein nonnegative selfadjoint extensions. Some conditions for the equality (L*(2)L1)* = L*(1)L2 are obtained. Applications to 1D nonnegative Hamiltonians, corresponding to point interactions, are given.

Functional models for Nevanlinna families

Behrndt J., Hassi S., Snoo H. de

Opuscula Mathematica

2008

Vol. 28, no. 3

233-245

The class of Nevanlinna families consists of R-symmetric holomorphic multivalued functions on C \ R with maximal dissipative (maximal accumulative) values on C+ (C-, respectively) and is a generalization of the class of operator-valued Nevanlinna functions. In this note Nevanlinna families are realized as Weyl families of boundary relations induced by multiplication operators with the independent variable in reproducing kernel Hilbert spaces.