  We study a special class of operators T satisfying the transmutation relation
(Tu)"-qTu=Tu" in the sense of distributions, where q is a locally integrable
function, and u belongs to a suitable space of distributions depending on the
smoothness properties of q. A method which allows one to construct a
fundamental set of transmutation operators of this class in terms of a single
particular transmutation operator is presented. Moreover, following [27], we
show that a particular transmutation operator can be realized as a Volterra
integral operator of the second kind. We study the boundedness and
invertibility properties of the transmutation operators, and used it to obtain
a representation for the general distributional solution of the equation
u"-qu=zu, in terms of the general solution of the same equation with z=0.
