대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제17권4호
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  • Pages.731-740
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  • 2002
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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GENERALIZED HERMITE INTERPOLATION AND SAMPLING THEOREM INVOLVING DERIVATIVES

  • 발행 : 2002.10.01
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초록

We derive the generalized Hermite interpolation by using the contour integral and extend the generalized Hermite interpolation to obtain the sampling expansion involving derivatives for band-limited functions f, that is, f is an entire function satisfying the following growth condition ｜f(ｚ)｜$\leq$ A exp($\sigma$｜y｜) for some A, $\sigma$ > 0 and any ｚ=$\varkappa$ + iy∈C.

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참고문헌

  1. Interpolation and Approximation P.J. Davis
  2. Foundations Sampling Theory in Fourier and Signal Analysis H.R. Higgins
  3. I.R.E. Trans. Inform. Theory v.IT-2 Some general aspects of the sampling theorem D.L. Jagerman;L.J. Fogel
  4. Inform. Control v.3 A generalization of the sampling theorem D.A. Linden;N.M. Abramson https://doi.org/10.1016/S0019-9958(60)90242-4
  5. Birkhoff Interpolation G.G. Lorentz;K. Jettler;S.D. Riemenschneider
  6. Theory and Practice Nonuniform Sampling F.A., Marvasti
  7. Inform. Control On sampling a function and its derivatives A. Nathan https://doi.org/10.1016/S0019-9958(73)90255-6
  8. Theor. Probability Appl. v.12 On the problem of interpolation of stochastic processes Z.A. Piranashvili https://doi.org/10.1137/1112079
  9. IEEE Trans. Inform. Theory v.IT-35 no.6 A Stable Nonuniform Sampling Expansion Involving Derivatives M.D. Rawn
  10. General Sampling Theorem Using Contour Integral C.E. Shin;S.Y. Chung;D. Kim https://doi.org/10.1016/j.jmaa.2003.10.042
  11. Advances in Shannon's Sampling Theory A.I. Zayed

피인용 문헌

  1. A Modification of Hermite Sampling with a Gaussian Multiplier vol.36, pp.4, 2015, https://doi.org/10.1080/01630563.2015.1013550
  2. Generalized sinc-Gaussian sampling involving derivatives vol.73, pp.4, 2016, https://doi.org/10.1007/s11075-016-0129-4
  3. Truncation error estimates for generalized Hermite sampling vol.74, pp.2, 2017, https://doi.org/10.1007/s11075-016-0159-y