Abstract
We are interested in finding necessary and sufficient conditions for irregular sampling to hold. We shall show that the inverse spectral problem can be used to construct sampling type theorems from the knowledge of the sampling points only. This improves Kramer's theorem as it reveals all possible distributions of the sampling points together with a construction of the sampling functions.
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Communicated by Paul L. Butzer
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Boumenir, A. Irregular sampling and the inverse spectral problem. The Journal of Fourier Analysis and Applications 5, 373–383 (1999). https://doi.org/10.1007/BF01259378
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DOI: https://doi.org/10.1007/BF01259378