Some algebraic relations between involutions, convolutions, and correlations, with applications to holographic memories.

Convolutions and correlations # in spaces H of doubly infinite sequences are related by a # b = S(a Sb), where S is an involution which reflects the order in the integral domain Z on which the sequences are defined. This relation can be used to represent a non-associative correlation algebra (H, #) by an associative convolution algebra equipped with the involution S which, as is shown, greatly simplifies derivations. Related matrix representations of #, S are given for sequences with finite support in Ren. Some implications for holographic memory models are discussed.