Given two arrays X nm and P nm describing two physical quantities, Heisenberg could form a new array of the same type by combining the terms X nk P km, which also oscillate with the right frequency. Since the Fourier coefficients of the product of two quantities is the convolution of the Fourier coefficients of each one separately, the correspondence with Fourier series allowed Heisenberg to deduce the rule by which the arrays should be multiplied, ( X P ) m n = ∑ ∑ k = 0 ∞ ∞ X m k P k n .