Resolvent estimates of the Dirac operator
Abstract
We shall investigate the asymptotic behavior of the extended resolvent R(s) of the Dirac operator as s increases to infinity, where s is a real parameter. It will be shown that the norm of R(s), as a bounded operator between two weighted Hilbert spaces of square integrable functions on the 3dimensional Euclidean space, stays bounded. Also we shall show that R(s) converges 0 strongly as s increases to infinity. This result and a result of Yamada [15] are combined to indicate that the extended resolvent of the Dirac operator decays much more slowly than those of Schroedinger operators.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 1999
 arXiv:
 arXiv:math/9902084
 Bibcode:
 1999math......2084P
 Keywords:

 Spectral Theory
 EPrint:
 28 pages, no figures