On the additive decomposition for polynomic maps

A polynomic operator can be represented as
T= L\tau
where τ is an imbedding of the input Hilbert resolution space into the appropriate Hilbert scale, and
L
is a mapping of the Hilbert resolution space that results from closing the span of the Hilbert scale with respect to a naturally defined inner product, into the output Hilbert resolution space. This paper demonstrates the relationship between the strongly causal (strongly anticausal, memoryless) components of
L
and
T
.