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Sampling and interpolation for a lacunary spectrum

Published online by Cambridge University Press:  14 November 2011

Yu. Lyubarskii  and
I. Spitkovsky
Yu. Lyubarskii
Affiliation:
Institute for Low Temperature Physics and Engineering, Academy of Science of Ukraine, 47, Lenin pr., Kharkov, 310164, Ukraine e-mail: lyubarskii@ilt.Kharkov.ue
I. Spitkovsky
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, VA 23187, U.S.A. e-mail; ilya@cs.wm.edu
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Abstract

We reduce the problem of constructing a sampling and interpolating set for the space of functions with limited multi-band spectra to a problem of invertibility of certain convolution operators on a system of intervals, and obtain an example of such a set located in a horizontal strip along the real axis. We also study the question of sampling of a signal with two-banded spectra via its values at the union of two arithmetic progressions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 1 , 1996 , pp. 77 - 87
Copyright
Copyright © Royal Society of Edinburgh 1996

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