JournalszaaVol. 12, No. 3pp. 511–534

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

  • L. Bezuglaya

    Kharkov State University, Ukraine
  • Victor Katsnelson

    Weizmann Institute of Science, Rehovot, Israel
The Sampling Theorem for Functions with Limited Multi-Band Spectrum I cover
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Abstract

In this paper functions ff belonging to L2(R)L^2(\mathbb R) are considered which spectrum is contained in a ’multi-band’ set EE, 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 L2(E)L^2(E). In the first part of this work we consider sets EE consisting of regularly positioned intervals of the same length.

Cite this article

L. Bezuglaya, Victor Katsnelson, The Sampling Theorem for Functions with Limited Multi-Band Spectrum I. Z. Anal. Anwend. 12 (1993), no. 3, pp. 511–534

DOI 10.4171/ZAA/550