SOME FUNCTIONAL INEQUALITIES WITH APPLICATION TO GREENS’ FUNCTIONS

摘要

Some elementary inequalities for functionals with functional derivatives of given sign are presented and proved. These are then applied to the study of Greens1 functions for diffusion processes in a medium with sources and sinks (or alternately Schrodinger operator Greens' functions). The resulting inequalities are shown to in¬clude as quite special cases the super - and sub -additive inequalities of potential theory. One consequence of the generalization is that the scattering length is also shown to have sub - additive properties.