Simplifications and clarifications on the paper ´An algebra of transfer functions for distributed linear time-invariant systems´

In this note we first point out some simplifications in some results of our paper mentioned above [1]. Second, we prove that the algebra of transfer functions , introduced in the paper, is in fact the quotient ring of the ring with respect to the multiplicative system defined in this note. The analogy between , seen as the quotient , and the algebra of proper rational functions seen as the quotient (where is the ring of proper rational functions analytic in , and is the multiplicative system of such functions tending to a nonzero constant as ), is fully developed and supports the claim that is a natural extension of the algebra of proper rational functions to distributed systems. These algebraic developments have been found most useful in applications [11], [12].