, Volume 13, Issue 2, pp 113-122

Convolution and correlation algebras

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An algebraic characterization of convolution and correlation is outlined. The basic algebraic structures generated on a suitable vector space by the two operations are described. The convolution induces an associative Abelian algebra over the real field; the correlation induces a not-associative, not-commutative — but Lieadmissible algebra — with a left unity. The algebraic connection between the two algebras is found to coincide with the relation of isotopy, an extension of the concept of equivalence. The interest of these algebraic structures with respect to information processing is discussed.