Balian–Low theorem

In mathematics, the Balian–Low theorem in Fourier analysis is named for Roger Balian and Francis E. Low.The theorem states that there is no well-localized window function (or Gabor atom) g either in time or frequency for an exact Gabor frame (Riesz Basis). In mathematics, the Balian–Low theorem in Fourier analysis is named for Roger Balian and Francis E. Low.The theorem states that there is no well-localized window function (or Gabor atom) g either in time or frequency for an exact Gabor frame (Riesz Basis). Suppose g is a square-integrable function on the real line, and consider the so-called Gabor system for integers m and n, and a,b>0 satisfying ab=1. The Balian–Low theorem states that if is an orthonormal basis for the Hilbert space