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On the regularized Whittaker-Kotel'nikov-Shannon sampling formula

Author: Liwen Qian
Journal: Proc. Amer. Math. Soc. 131 (2003), 1169-1176
MSC (2000): Primary 41A80, 41A30; Secondary 65D25, 65G99, 94A24
Published electronically: October 24, 2002
MathSciNet review: 1948108
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Abstract | References | Similar Articles | Additional Information

Abstract: Error estimation is given for the regularized Whittaker-Kotel'nikov-Shannon (WKS) sampling formula, which was found to be accurate and robust for numerically solving partial differential equations. The result improves the convergence rate of existing results.

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  • 1. E. T. Whittaker, On the functions which are represented by the expansion of the interpolation theory, Proc. Roy. Soc. Edinburgh, sec. A, 35 (1915), 181-194.
  • 2. V. Kotel'nikov, On the carrying capacity of the ``ether" and wire in telecommunications, material for the first All-Union Conference on Questions of Communications, Izd. Red. Upr. Svyazi RKKA, Moscow, Russian (1933).
  • 3. C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), 379-423.
  • 4. Robert J. Marks II, Introduction to Shannon sampling and interpolation theory, Springer Texts in Electrical Engineering, Springer-Verlag, New York, 1991. MR 1077829
  • 5. Ahmed I. Zayed, Advances in Shannon’s sampling theory, CRC Press, Boca Raton, FL, 1993. MR 1270907
  • 6. J. R. Higgins, Sampling theory in Fourier and signal analysis : foundations, Oxford University Press, 1996.
  • 7. D. Jagerman, Bounds for truncation error of the sampling expansion, SIAM J. Appl. Math. 14 (1966), 714–723. MR 0213816,
  • 8. P. L. Butzer and R. L. Stens, A modification of the Whittaker-Kotelnikov-Shannon sampling series, Aequationes Math. 28 (1985), no. 3, 305–311. MR 791632,
  • 9. Robert Gervais, Qazi Ibadur Rahman, and Gerhard Schmeisser, A bandlimited function simulating a duration-limited one, Anniversary volume on approximation theory and functional analysis (Oberwolfach, 1983) Internat. Schriftenreihe Numer. Math., vol. 65, Birkhäuser, Basel, 1984, pp. 355–362. MR 820536
  • 10. G. W. Wei, D. S. Zhang, D. J. Kouri and D. K. Hoffman, Lagrange Distributed Approximating Functionals, Phys. Rev. Lett. 79 (1997), 775-779.
  • 11. G. W. Wei, Quasi wavelets and quasi interpolating wavelets, Chem. Phys. Lett. 296 (1998), 215-222.
  • 12. G. W. Wei, Discrete singular convolution for the sine-Gordon equation, Phys. D 137 (2000), no. 3-4, 247–259. MR 1740097,
  • 13. G. W. Wei, Solving quantum eigenvalue problems by discrete singular convolution, J. Phys. B 33 (2000), 343-359.
  • 14. Shuguang Guan, C.-H. Lai, and G. W. Wei, Fourier-Bessel analysis of patterns in a circular domain, Phys. D 151 (2001), no. 2-4, 83–98. MR 1834041,
  • 15. H. D. Pollak, A Remark on `Elementary Inequalities for Mills' Ratio' by Yûsaku Komatu, Rep. Stat. Appl. Res., JUSE 4:3 (1956). MR 18:722a
  • 16. Earl D. Rainville, Special functions, The Macmillan Co., New York, 1960. MR 0107725
    Earl D. Rainville, Special functions, 1st ed., Chelsea Publishing Co., Bronx, N.Y., 1971. MR 0393590

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Additional Information

Liwen Qian
Affiliation: Department of Computational Science, National University of Singapore, Singapore 117543
Address at time of publication: Singapore–MIT Alliance (SMA), E4-4-10, National University of Singapore, Singapore 117576

Keywords: Whittaker-Kotel'nikov-Shannon's sampling formula, regularization, error estimate
Received by editor(s): April 23, 2001
Received by editor(s) in revised form: November 8, 2001
Published electronically: October 24, 2002
Communicated by: David Sharp
Article copyright: © Copyright 2002 American Mathematical Society