Riesz Sequence - Theorems

Theorems

If H is a finite-dimensional space, then every basis of H is a Riesz basis.

Let φ be in the Lp space L2(R), let

and let denote the Fourier transform of φ. Define constants c and C with . Then the following are equivalent:

The first of the above conditions is the definition for (φ_n) to form a Riesz basis for the space it spans.