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A modification of the Whittaker-Kotelnikov-Shannon sampling series

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References

  1. Aczél, J.,Vorlesungen über Funktionalgleichungen und ihre Anwendungen. Birkhäuser, Basel, 1961.

    Google Scholar 

  2. Aczél, J. andDaróczy, Z.,On measures of information and their characterizations. Academic Press, New York-London, 1975.

    Google Scholar 

  3. Butzer, P. L.,A survey of the Whittaker-Shannon sampling theorem and some of its extensions. J. Math. Res. Exposition3 (1983), 185–212.

    Google Scholar 

  4. Butzer, P. L. andNessel, R. J.,Fourier analysis and approximation. Birkhäuser, Basel; Academic Press, New York, 1971.

    Google Scholar 

  5. Butzer, P. L. andStens, R. L.,The Poisson summation formula, Whittaker's cardinal series and approximate integration. InProc. Second Edmonton Conf. on Approximation Theory (Edmonton, Canada, June 1982), Amer. Math. Soc., Providence, R.I., 1983, pp. 19–36.

  6. Campbell, L.L.,Sampling theorem for the Fourier transform of a distribution with bounded support. SIAM J. Appl. Math.16 (1968), 626–636.

    Google Scholar 

  7. Dickmeis, W. andNessel, R. J.,A unified approach to certain counterexamples in approximation theory in connection with a uniform boundedness principle with rates. J. Approx. Theory31 (1981), 161–174.

    Google Scholar 

  8. Gervais, R., Rahman, Q. I. andSchmeisser, G.,A bandlimited function simulating a duration-limited one. InAnniversary Volume on Approximation Theory and Functional Analysis (Proc. Internat. Conf., Oberwolfach, Germany, July/August 1983), Birkhäuser, Basel, 1984, pp. 355–362.

    Google Scholar 

  9. Jagerman, D.,Bounds for truncation error of the sampling expansion. SIAM J. Appl. Math.14 (1966), 714–723.

    Google Scholar 

  10. Junggeburth, J., Scherer, K. andTrebels, W.,Zur besten Approximation auf Banachräumen mit Anwendungen auf ganze Funktionen. Forschungsber. des Landes Nordrhein-Westfalen2311 (1973), 51–75.

    Google Scholar 

  11. Nikol'skii, S. M.,Approximation of functions of several variables and imbedding theorems. Springer, New York-Heidelberg, 1975.

    Google Scholar 

  12. Schönhage, A.,Approximationstheorie. De Gruyter & Co., Berlin, 1975.

    Google Scholar 

  13. Splettstösser, W., Stens, R. L. andWilmes G.,On approximation by the interpolating series of G. Valiron. Funct. Approx. Comment. Math.11 (1981), 39–56.

    Google Scholar 

  14. Stens, R. L.,Error estimates for sampling sums based on convolution integrals. Inform. and Control45 (1980), 37–47.

    Google Scholar 

  15. Stens, R. L.,Approximation of functions by Whittaker's cardinal series. InGeneral Inequalities 4 (Proc. Internat. Conf., Oberwolfach, Germany, April/May 1983), Birkhäuser, Basel, 1984, pp. 137–149.

    Google Scholar 

  16. Timan, A. F.,Theory of approximation of functions of a real variable. Pergamon, Oxford, 1963.

    Google Scholar 

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Dedicated to Professor János Aczél on his 60th birthday

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Butzer, P.L., Stens, R.L. A modification of the Whittaker-Kotelnikov-Shannon sampling series. Aeq. Math. 28, 305–311 (1985). https://doi.org/10.1007/BF02189424

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  • DOI: https://doi.org/10.1007/BF02189424

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