ABSTRACT

T h i s means that F = C A , where A = E H o 1 7 ^ ? ^ L 2 ( R ) . T h i s impl ies tha t A is i n V'L2. •

W e are able to form a s imilar theorem for the C a r l e m a n t ransformat ion.

THEOREM 6.15.5. A function F in H(IL~ U l l + ) is the Carleman transform of a slowly increasing function f iff F may be written in the form (6.15.6), where the function Fv fulfils (6.15.5).