The problem now lies in finding the Green's function G that satisfies equation (1).

The dual function g is concave, even when the initial problem is not convex.

The representing function g is the impulse response of the transformation S.

If n is the order of pole a, then necessarily g(a) 0 for the function g in the above expression.

So that the function G has a logarithmic divergence both at small and large r.

The function g is a continuous replacement for the function f.

That function g is then called the inverse of f, and usually denoted as f.

The function g gives rise to a germ, and the product of fg is equal to 1.

As in the case of a single function "g", this implies the required inequality.

The function g might represent the transfer function of an instrument or a driving force that was applied to a physical system.