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Zeitschrift für Analysis und ihre Anwendungen

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Volume 12, Issue 3, 1993, pp. 511–534
DOI: 10.4171/ZAA/550

Published online: 1993-09-30

The Sampling Theorem for Functions with Limited Multi-Band Spectrum I

L. Bezuglaya[1] and Victor Katsnelson[2]

(1) Kharkov State University, Ukraine
(2) Weizmann Institute of Science, Rehovot, Israel

In this paper functions $f$ belonging to $L^2(\mathbb R)$ are considered which spectrum is contained in a ’multi-band’ set $E$, i.e. in a subset of the real axis which is the union of finite many intervals. For such functions a generalization of the Whittaker-Kotelnikov-Shannon sampling formula is given. The considered problem is also related to Riesz bases of exponentials in $L^2(E)$. In the first part of this work we consider sets $E$ consisting of regularly positioned intervals of the same length.

Keywords: Multi-band spectrum, square-summable entire functions, interpolation of entire functions, the sampling formula, bases of exponentials in $L^2$, cardinal series

Bezuglaya L., Katsnelson Victor: The Sampling Theorem for Functions with Limited Multi-Band Spectrum I. Z. Anal. Anwend. 12 (1993), 511-534. doi: 10.4171/ZAA/550