The spinless Salpeter equation presents a rather particular differenti
al operator. In this paper we rewrite this equation into integral and
integro-differential equations. These kinds of equations are well know
n and can be more easily handled. We also present some analytical resu
lts concerning the spinless Salpeter equation and the action of the sq
uare-root operator. (C) 1998 American Institute of Physics. [S0022-248
8(98)00403-4].