论文信息 - Some algebraic relations between involutions, convolutions, and correlations, with applications to holographic memories

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

Convolutions * and correlations # in spacesH of doubly infinite sequences are related bya#b=S(a * Sb), whereS is an involution which reflects the order in the integral domainZ 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 involutionS 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.

P. H. Schönemann | P. Schönemann

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