Riesz sequence
In mathematics, a sequence of vectors in a Hilbert space is called a Riesz sequence if there exist constants such that
for all sequences of scalars in the ℓp space ℓ2. A Riesz sequence is called a Riesz basis ifTheorems
If H is a finite-dimensional space, then every basis of H is a Riesz basis.
Let be in the Lp space L2, let
and let denote the Fourier transform of. Define constants c and C with. Then the following are equivalent:
The first of the above conditions is the definition for to form a Riesz basis for the space it spans.
