XIX Int. Congress on Nuclear and Aerospace Electronics, Rome 1971.
A rule exists to distill a Multidimensional Laplace Transform (MLT) down to one dimension corresponding to real time, in this conference paper I suggested a complementary rule to reconstruct an MLT expression.
The behavior of dynamic linear systems is described by a one-dimensional function, nonlinear systems require more dimensions to describe their behavior. Multidimensional Laplace Transform (MLT) is the nonlinear representation of the one dimensional Laplace Transform familiar to engineering undergraduates in the analysis of linear systems. In order to convert an MLT expression to a single time dimension the Laplace variables have to be associated, usually by following a simple inspection rule. Here, I suggest that the reverse is also possible, i.e. to create or synthesize a multiple dimensional kernel from a single Laplace variable.
An interesting corollary to the inspection rule of dissociation of variables suggests that higher dimensional kernels can be reduced in complexity to two dimensions: One dimension along the diagonal and identical functions along all dimensions higher than the second.
