Journal of Integral Equations and Applications

On the Use of Green's Function in Sampling Theory

M.H. Annaby and A.I. Zayed

Full-text: Open access

Article information

Source
J. Integral Equations Applications Volume 10, Number 2 (1998), 117-139.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
http://projecteuclid.org/euclid.jiea/1181074218

Digital Object Identifier
doi:10.1216/jiea/1181074218

Mathematical Reviews number (MathSciNet)
MR1646834

Zentralblatt MATH identifier
0917.41002

Subjects
Primary: 41A05: Interpolation [See also 42A15 and 65D05]
Secondary: 34B05: Linear boundary value problems

Keywords
Boundary-value problems Kramer's sampling theorem

Citation

Annaby, M.H.; Zayed, A.I. On the Use of Green's Function in Sampling Theory. J. Integral Equations Applications 10 (1998), no. 2, 117--139. doi:10.1216/jiea/1181074218. http://projecteuclid.org/euclid.jiea/1181074218.


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References

  • M.H. Annaby and M.A. El-Sayed, Kramer-type sampling theorems associated with Fredholm integral operators, Methods Appl. Anal. 2 (1995), 76-91.
  • H.E. Benzinger, Green's function of ordinary differential operators, J. Differential Equations 7 (1970), 478-496.
  • --------, Pointwise and norm convergence of a class of biorthonormal expansions, Trans. Amer. Math. Soc. 231 (1977), 259-271.
  • G.D. Birkhoff, Boundary value and expansion problems of ordinary linear differential equations, Trans. Amer. Math. Soc. 9 (1908), 373-395.
  • 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.
  • J.A. Cochran, The analysis of linear integral equations, McGraw-Hill, New York, 1972.
  • E.A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955.
  • W.N. Everitt, G. Schöttler and P.L. Butzer, Sturm-Liouville boundary value problems and Lagrange interpolation series, Rend. Mat. Appl. (7) 14 (1994), 87-126.
  • J.R. Higgins, Sampling theory in Fourier and signal analysis: Foundations, Oxford University Press, Oxford, 1996.
  • J.W. Hopkins, Some convergent developments associated with irregular boundary conditions, Trans. Amer. Math. Soc. 20 (1919), 245-259.
  • V.P. Mihailov, Riesz bases in $L^2(0,1)$, Soviet Math. 3 (1962), 851-855.
  • M.A. Naimark, Linear differential operators: Part I, George Harrap, London, 1967.
  • I. Stakgold, Green's functions and boundary value problems, Wiley, New York, 1979.
  • M.H. Stone, A comparison of the series of Fourier and Birkhoff, Trans. Amer. Math. Soc. 28 (1926), 695-761.
  • J.D. Tamarkin, Some general problems of the theory of ordinary linear differential equations and expansion of an arbitrary function in series of fundamental functions, Math. Z. 27 (1927), 1-54.
  • W. Ward, An irregular boundary value and expansion problem, Ann. Math. 26 (1925), 21-36.
  • A.I. Zayed, A new role of Green's function in interpolation and sampling theory, J. Math. Anal. Appl. 175 (1993), 222-238.
  • A.I. Zayed, M.A. El-Sayed and M.H. Annaby, On Lagrange interpolations and Kramer's sampling theorem associated with self-adjoint boundary value problems, J. Math. Anal. Appl. 158 (1991), 269-284.