Boolean functions with small spectral norm

Let f : F-2(n) ->{0, 1} be a boolean function, and suppose that the spectral norm parallel to f parallel to(A) := Sigma(r) vertical bar(f) over cap (r)vertical bar of f is at most M. Then [GRAPHICS] where L <= 2(2CM4) and each H-j is a subgroup of F-2(n). This result may be regarded as a quantitative analogue of the Cohen Helson - Rudin structure theorem for idempotent measures in locally compact abelian groups.