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).

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 then either The Balian–Low theorem has been extended to exact Gabor frames.

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