the set of all elements a + b where a is in A and b is in B; and similarly A − B for the set of differences a − b. For any element e in A, Dyson's transform consists in forming the sequences and . The transformed sequences have the properties:

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Other closely related transforms are sometimes referred to as Dyson transforms. This includes the transform defined by , , , for sets in a (not necessarily abelian) group. This transformation has the property that

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