Self-adjointness via partial Hardy-like inequalities
Analysis of PDEs
2017-08-23 v1 Mathematical Physics
math.MP
Spectral Theory
Abstract
Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality. Particular cases are Dirac-Coulomb operators where distinguished selfadjoint extensions are obtained for the optimal range of coupling constants.
Cite
@article{arxiv.0805.4675,
title = {Self-adjointness via partial Hardy-like inequalities},
author = {Maria J. Esteban and Michael Loss},
journal= {arXiv preprint arXiv:0805.4675},
year = {2017}
}