III.91 Transforms by T. W. Körner: Pages 303 – 304.

Transforms by T. W. Körner.  If a is a sequence a0, a1, a2, …, we can define an “infinite polynomial” (Ga)(t) to be S¥r=0 artr.  We need to worry about in what sense this sum exists.  Formally, (Ga)(t)(Gb)(t) = (G(a*b))(t), where the infinite sequence c = a * b is given by ck = a0bk + a1bk-1 + … + akb0 .  We call this the convolution of a and b.

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