id: 05804456
dt: j
an: 05804456
au: Lammers, Mark; Maeser, Anna
ti: An uncertainty principle for finite frames.
so: J. Math. Anal. Appl. 373, No. 1, 242-247 (2011).
py: 2011
pu: Elsevier, San Diego, CA
la: EN
cc: 
ut: frames; Gauss-Hermite differential equation; time-frequency dual;
    uncertainty principle
ci: 
li: doi:10.1016/j.jmaa.2010.06.048
ab: In this article the authors define an uncertainty principle for finite
    frames. They begin by developing a time-frequency localization measure
    for the entire frame using a difference operator. Then they prove that
    a subset of columns of the discrete Fourier transform matrix are
    optimal for minimizing this measure over all equal norm Parseval
    frames. This gives a sharp constant for the lower bound which is
    dependent on the dimension of the space and the number of elements in
    the frame. The authors also find a minimizer and bounds for the
    time-frequency measure in the case of Parseval frames which are not
    necessarily equal norm. Next they show that given any matrix whose
    columns form a frame, it is possible to generate a dual frame that
    minimizes the finite time-frequency measure. Finally, to illustrate
    this, the authors generate a random frame and compare the
    time-frequency localization of this dual with the canonical one.
rv: Magali Anastasio (Buenos Aires)