Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.
@article{bwmeta1.element.bwnjournal-article-amcv17i2p143bwm,
author = {Avdonin, Sergei and Bulanova, Anna and Moran, William},
title = {Construction of sampling and interpolating sequences for multi-band signals. the two-band case},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {17},
year = {2007},
pages = {143-156},
zbl = {1275.94020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv17i2p143bwm}
}
Avdonin, Sergei; Bulanova, Anna; Moran, William. Construction of sampling and interpolating sequences for multi-band signals. the two-band case. International Journal of Applied Mathematics and Computer Science, Tome 17 (2007) pp. 143-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv17i2p143bwm/
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