Construction of Sampling and Interpolating Sequences for Multi-Band Signals. The Two-Band Case

Authors:
Sergei Avdonin;Anna Bulanova;William Moran
Affiliations:
Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775-6660, USA;Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775-6660, USA;Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne Victoria 3010, Australia
Venue:
International Journal of Applied Mathematics and Computer Science
Year:
2007

Citing 2
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Abstract

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.