Theorem 1 (Balian-Low)

Suppose gL2(R) and gm,n(x)=e2πimxg(x-n), where m,nZ. If {gm,n:m,nZ} is an orthonormal basis for L2(R), then either

-x2|g(x)|2𝑑x= or -ξ2|g^(ξ)|2𝑑ξ=.
Title Balian-Low
Canonical name BalianLow
Date of creation 2013-03-22 15:35:12
Last modified on 2013-03-22 15:35:12
Owner swiftset (1337)
Last modified by swiftset (1337)
Numerical id 4
Author swiftset (1337)
Entry type Theorem
Classification msc 42C10