Resolvent estimates of the Dirac operator

Pladdy, Chris; Saito, Yoshimi; Umeda, Tomio

Resolvent estimates of the Dirac operator

Authors

Pladdy, Chris

Saito, Yoshimi

Umeda, Tomio

Description

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 3-dimensional 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.
28 pages, no figures