Abstract
For a periodic nonuniform sampling set \(\Lambda =\{x_n+\rho \ell :1\le n\le L,~l\in {\mathbb {Z}}\}\) of period \(\rho \) with length L, we discuss the problem of sampling and interpolation involving derivative samples in the Paley-Wiener space \({\mathcal {P}}{\mathcal {W}}_{2\pi \sigma }.\) Using block Laurent operators, we provide a complete characterization of sampling and interpolation in terms of period, length, and the number of derivative samples.
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Acknowledgements
The authors would like to thank anonymous reviewer for meticulously reading the manuscript and giving us valuable suggestions and comments to improve the earlier version of the manuscript to the present stage. The second author acknowledges the funding support provided by Indian Institute of Technology Dhanbad under FRS with Grant No. FRS(134)/2019-2020/AM.
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Ghosh, R., Selvan, A.A. Sampling and Interpolation of Periodic Nonuniform Samples Involving Derivatives. Results Math 78, 52 (2023). https://doi.org/10.1007/s00025-022-01826-x
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DOI: https://doi.org/10.1007/s00025-022-01826-x
Keywords
- Beurling density
- derivative sampling
- Laurent operators
- Paley-Wiener space
- periodic nonuniform samples
- Zak transform