This can be generalized to any function F of an operator:

The characteristic function F of a set S is defined as:

Every function F 1 of S can be written as a product of primitive functions.

The function F must be discretized spatially with a central difference.

In effect, we have a user defined function F with two arguments.

So the function F must be nonlinear to create heterodynes (mixer products).

A function F such that for all e is called fixed point free.

Standard assumptions on the form of the function F(.)

The function F is some nonlinear function, such as a polynomial.

For other values of x and y the function F can be defined by analytic continuation.