Abstract
This paper discusses the extension of the Kramer sampling theorem to the case when the kernel is Cauchy analytic in the sampling parameter.
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P.L. Butzer and G. Nasri-Roudsari. ‘Kramer’s sampling theorem in signal analysis and its role in mathematics.’ In Image Processing; Mathematical Methods and Applications. (Proc. Conf. Cranfield University, UK; ed. J.M. Blackledge; Oxford University Press, 1994.)
P.L. Butzer and G. Schöttler. ‘Sampling theorems associated with fourth and higher order self-adjoint eigenvalue problems’. J. Comput. Appl Math. 51 (1994), 159–177.
P.L. Butzer, W. Splettstösser and R.L. Stens. ‘The sampling theorem and linear prediction in signal analysis.’ Jahresber. Deutsch. Math.-Verein. 90 (1988), 1–70.
L.L. Campbell. ‘A comparison of the sampling theorems of Kramer and Whittaker.’ J. SIAM 12 (1964), 117–130.
E.A. Coddington and N. Levinson. Theory of Ordinary Differential Equations (McGraw-Hill, New York, 1995).
E.T. Copson. Theory of Functions of a Complex Variable (Oxford University Press, 1944).
W.N. Everitt and W.K. Hayman. ‘On a non-regular parametric integral IL’ (To appear in a volume of papers dedicated to Matts Essen; to be published by The University of Uppsala, Sweden, 1998.)
W.N. Everitt, W.K. Hayman and G. Nasri-Roudsari. ‘On the representation of holomorphic functions by integrals.’ Appl Anal 65 (1997), 95–102.
W.N. Everitt and G. Nasri-Roudsari. ‘Interpolation and sampling theories, and linear boundary value problems.’ (To appear in reference [12] below.)
W.N. Everitt, G. Schüttler and P.L. Butzer. ‘Sturm-Liouville boundary value problems and Lagrange interpolation series.’ Rend. Math. Appl (7)14 (1994), 87–126.
J.R. Higgins. Sampling Theory in Fourier and Signal Analysis: Foundations. (Clarendon Press, Oxford, 1996).
J.R. Higgins and R.L. Stens. Sampling Theory in Fourier and Signal Analysis: Advanced Topics. (Clarendon Press, Oxford, to appear).
T. Kato. Perturbation Theory for Linear Operators. (Springer-Verlag, Heidelberg; 1984.)
H.P. Kramer. ‘A generalized sampling theorem.’ J. Math. Phys. 38 (1959), 68–72.
E.C. Titchmarsh. The Theory of Functions. (Oxford University Press, 1939).
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This paper is dedicated to Professor P.L. Butzer on the occasion of his 70th birthday
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Everitt, W.N., Nasri-Roudsari, G. & Rehberg, J. A note on the analytic form of the Kramer sampling theorem. Results. Math. 34, 310–319 (1998). https://doi.org/10.1007/BF03322057
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DOI: https://doi.org/10.1007/BF03322057