Translation invariance means that continuous matrix multiplication, C ( x , x ″ ) = ∫ ∫ x ′ A ( x , x ′ ) B ( x ′ , x ″ ) , is essentially convolution, C ( Δ Δ ) = C ( x − − x ″ ) = ∫ ∫ x ′ A ( x − − x ′ ) B ( x ′ − − x ″ ) = ∫ ∫ y A ( Δ Δ − − y ) B ( y ) .