Geodesic
Reconstruction of Entire Functions From Irregularly Spaced Sample Points
Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 777-793

Voir la notice de l'article provenant de la source Cambridge University Press

Let where {λn }n ∈ Ζ is a sequence of real numbers such that |λn — n| ≤ Δ for some Δ > 0 and all n ∈ Z . Extending an obvious property of sin πz to which the function G reduces when Δ = 0 we show that is bounded by a constant independent of n. The result is then applied to a problem concerning derivative sampling in one and several variables.
DOI : 10.4153/CJM-1996-040-7
Mots-clés : 30D10, 30D15, 41A05, 94A05, entire functions of exponential type, Whittaker-Shannon sampling theorem, nonuniform sampling, multidimensional sampling, interpolation 
Grozev, Georgi R.; Rahman, Qazi I. Reconstruction of Entire Functions From Irregularly Spaced Sample Points. Canadian journal of mathematics, Tome 48 (1996) no. 4, pp. 777-793. doi: 10.4153/CJM-1996-040-7
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[1] 1. Ahiezer, N.I., On the interpolation of entire transcendental functions of finite order, Dokl. Akad. Nauk, SSSR(N.S.) 65(1949), 781–784. Google Scholar

[2] 2. Boas, R.P., Jr., Integrability along a line for a class of entire functions, Trans. Amer. Math. Soc. 73(1952), 191–197. Google Scholar

[3] 3. Boas, R.P., Entire functions, Academic Press, New York, (1954). Google Scholar

[4] 4. Butzer, P.L. and Hinsen, G., Two-dimensional nonuniform sampling expansions —An iterative approach. I. Theory of two-dimensional bandlimited signals. II.Reconstruction formulae and applications, Appl. Anal., 32(1989), 53–67. 69-85. Google Scholar

[5] 5. Duffin, R.J. and Schaeffer, A.C., class ofnonharmonic Fourier series, Trans. Amer. Math. Soc. 72(1952), 341–366. Google Scholar

[6] 6. Fichtenholz, G.M., Differential und Integralrechnung, VEB Deutscher Verlag der Wissenschaften, Berlin 1(1966). Google Scholar

[7] 7. Higgins, J.R., A sampling theorem for irregularly spaced sample points, IEEE Trans. Inform. Theory, IT- 22(1976), 621–622. Google Scholar

[8] 8. Higgins, J.R., Sampling theorems and the contour integral method, Appl. Anal. 41(1991), 155–168. Google Scholar

[9] 9. Hinsen, G., Irregular Sampling of Bandlimited IP —functions, J. Approx., Theory, 72(1993), 346–364. Google Scholar

[10] 10. Ya, B.. Levin, On functions of finite degree, bounded on a sequence of points, Dokl. Akad. Nauk SSSR, (N.S.) 65(1949), 265–268. Google Scholar

[11] 11. Levinson, N., Gap and density theorems, Amer. Math. Soc. Colloquium Publications, New, York 26(1940). Google Scholar

[12] 12. Nikol'skiĭ, S.M., Approximation of functions of several variables and imbedding theorems, Springer-Verlag, Berlin, Heidelberg, New York, 1975. Google Scholar

[13] 13. Plancherel, M. and Pólya, G., Fonctions entières et intégrates de Fourier multiples, Comment. Math. Helv. 9(1937),, 224–248. 10(1938), 110–163. Google Scholar

[14] 14. Rahman, Q.I., Interpolation of entire functions, Amer. J., Math. 87(1965), 1029–1076. Google Scholar

[15] 15. Rahman, Q.I. and Schmeisser, G., IP inequalities for entire functions of exponential type, Trans. Amer. Math., Soc. 320(1990), 91–103. Google Scholar

[16] 16. Ronkin, L.I., Introduction to the theory of entire functions of several variables, Amer. Math. Soc. Transl. of Math. Monographs, Rhode, Island 44(1974). Google Scholar

[17] 17. Titchmarsh, E.C., The theory of functions, 2d ed.Oxford University Press, 1939. Google Scholar

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