Self-adjointness via Hardy-like inequalities

Maria J. Esteban (1) , Michael Loss (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 School of Mathematics - Georgia Institute of Technology

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.

Mots clés: Relativistic quantum mechanics; Dirac operator; self-adjoint operator; self-adjoint extension; Schur complement.; Schur complement

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Maria J. Esteban, Michael Loss. Self-adjointness via Hardy-like inequalities. QMATH10, 2007, Moeciu, Romania. pp.41-47. ⟨hal-00283411⟩