Peter H. Schönemann
Professor Emeritus • Department of Psychological Sciences • Purdue University

Abstract 49


Peter H. Schonemann

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

Biological Cybernetics, 1987, 56, 367-374


Convolutions * and correlations # in spaces H of doubly infinite sequences are related by a#b = S(a*b), 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 memories are discussed.