ISSN:
1531-5851
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this article a generalized sampling theorem using an arbitrary sequence of sampling points is derived. The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems. The theorem is then used to characterize a class of entire functions that can be reconstructed from their sample values at the points tn = an + b if n = 0, 1, 2, ... and tn = an + c if n = 0, -1, -2, ..., where a, b, c are arbitrary constants. The reconstruction formula is derived explicitly in the form of a sampling series expansion. When a = 1, b = 0 = c, the famous Whittaker-Shannon-Kotel'nikov sampling theorem is obtained as a special case.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s00041-001-4034-3
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