In this paper functions belonging to are considered which spectrum is contained in a ’multi-band’ set , 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 . In the first part of this work we consider sets consisting of regularly positioned intervals of the same length.
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L. Bezuglaya, Victor Katsnelson, The Sampling Theorem for Functions with Limited Multi-Band Spectrum I. Z. Anal. Anwend. 12 (1993), no. 3, pp. 511–534DOI 10.4171/ZAA/550