A Riesz basis of a Hilbert space is the image of an orthonormal basis under a bounded invertible
linear operator. Equivalently, a complete family
is a Riesz basis when there are
constants 
such that
 |
for every finitely supported scalar family 
(Christensen 2016). Completeness is required, since the
inequalities alone define a Riesz sequence.
A Riesz basis need not be orthogonal. For exponential functions in 
, the corresponding frequency
set is a Riesz spectrum.
