Riesz sequence
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A sequence of vectors (xn) in a Hilbert space H is called a Riesz sequence if there exist constants 
such that
for all sequences of scalars 
. A Riesz sequence is called a Riesz basis if
.
[edit] Theorems
If H is a finite-dimensional space, then every basis of H is a Riesz basis.
Let 
, φn(x) = φ(x − n) and 
be the Fourier transform of φ. Define constants c and C sch that . Then the following are equivalent:
The first of the above conditions is the definition for {φn} to form a Riesz basis for the space it spans.
[edit] See also
This article incorporates material from Riesz sequence on PlanetMath, which is licensed under the GFDL.
This article incorporates material from Riesz basis on PlanetMath, which is licensed under the GFDL.
