Young Scientist Excellence in Conference on Stochastic and Analytic Methods in Mathematical Physics (09.3.3-LMT-K-712-13-0025)

This project is funded by the European Social Fund.

The classical restriction-extension theory of symmetric operators is limited for describing supersingular perturbations in that a symmetric restriction of a self-adjoint operator is essentially self-adjoint in the reference Hilbert space. The typical example of a supersingular perturbation is the point-interaction associated with a Laplace operator in higher dimensions. To deal with supersingular perturbations one studies (Gelfand) triplet extensions instead. In this project we consider the so-called peak model (as opposed to the cascade model) for the triplet extensions of supersingular perturbations in the case of a not necessarily semibounded symmetric operator with finite defect numbers. The triplet extensions in scales of Hilbert spaces are described by means of abstract boundary conditions. The resolvent formulas of Krein-Naimark type are presented in terms of the gamma-field and the abstract Weyl function. The transformations to the reference Hilbert space that preserve the Weyl function are also considered.

Duration: 4 months (2019-05-07 – 2019-09-07)
Participant: doktorantas Rytis Juršėnas