Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms

V. I. Burenkova1 and W. D. Evansa1

a1 School of Mathematics, University of Wales–Cardiff, Senghennydd Road, Cardiff CF2 4YH, U.K.


The norm of an integral operator occurring in the partial wave decomposition of an operator B introduced by Brown and Ravenhall in a model for relativistic one-electron atoms is determined. The result implies that B is non-negative and has no eigenvalue at 0 when the nuclear charge does not exceed a specified critical value.

(Received March 06 1997)

(Revised November 03 1997)