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Sampling theorems associated with differential operators with finite rank perturbations

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We derive a sampling theorem associated with first order self-adjoint eigenvalue problem with a finite rank perturbation. The class of the sampled integral transforms is of finite Fourier type where the kernel has an additional perturbation.

Abstract

We derive a sampling theorem associated with first order self-adjoint eigenvalue problem with a finite rank perturbation. The class of the sampled integral transforms is of finite Fourier type where the kernel has an additional perturbation.

참고문헌 (27)

  1. M. H. Annaby, "On sampling theory associated with the resolvents of singular SturmLiouville problems", Proc. Amer. Math. Soc, 131(6), pp.1803~1812 (2003)
  2. M. H. Annaby, "Discontinuous boundary-value problems:Expansion and sampling theorems", J. Integral Equations Appl, 16(1), pp.1~23 (2004)
  3. M. H. Annaby, "A sampling theorem associated with boundary-value problems with not necessarily simple eigenvalues", Int. J. Math. Math. Sci, 21(3), pp.571~580 (1998)
  4. M. H. Annaby, "Perturbed discrete Sturm-Liouville problems and associated sampling theorems", Rocky Mountain J. Math, 39(6), pp.1781~1807 (2009)
  5. M. H. Annaby, "A perturbed Whittaker-Kotel’nikov-Shannon sampling theorem", J. Math. Anal. Appl, 381(1), pp.64~79 (2011)
  6. M. H. Annaby, "On the use of Green’s function in sampling theory", J. Integral Equations Appl, 10(2), pp.117~139 (1998)
  7. R. Boas, "Entire Functions" (1954), Academic Press
  8. P. L. Butzer, "Fourier Analysis and Approximation" (1971), Birhkh¨auser
  9. P. L. Butzer, "An introduction to sampling analysis", pp.2001, Kluwer
  10. P. L. Butzer, "Sampling theorems associated with fourth and higher order self-adjoint eigenvalue problems", J. Comput. Appl. Math, 51(2), pp.159~177 (1994)
  11. L. L. Campbell, "A comparison of the sampling theorems of Kramer and Whittaker", SIAM J. Appl. Math, 12, pp.117~130 (1964)
  12. E. A. Catchpole, "A Cauchy problem for an ordinary integro-differential equation", Proc. Roy. Soc. Edinburgh Sect. A, 72(1), pp.39~55 (1974)
  13. J. A. Cochran, "The Analysis of Linear Integral Equations" (1972), McGraw-Hill
  14. W. N. Everitt, "Sturm-Liouville problems with coupled boundary conditions and Lagrange interpolation series", J. Comput. Anal. Appl, 1(4), pp.319~347 (1999)
  15. W. N. Everitt, "Sturm-Liouville problems with coupled boundary conditions and Lagrange interpolation series II", Rend. Mat. Appl, 20, pp.199~238 (2000)
  16. W. N. Everitt, "Kramer analytic kernels and first-order boundary value problems", J. Comput. Appl. Math, 148(1), pp.22~47 (2002)
  17. I. Gohberg, "Basic Operator Theory" (1980), Birkh¨auser
  18. A. H. Haddad, "General methods for the derivation of sampling theorems", IEEE Trans. Inform. Theory, 13, pp.227~230 (1967)
  19. J. R. Higgins, "Sampling Theorey in Fourier and Signal Analysis: Foundations" (1996), Oxford University Press
  20. V. Kotel’nikov, "On the carrying capacity of the ether and wire in telecommunications", (Russian) Material for the first all union conference on questions of communications (1933)
  21. M. A. Naimark, "Linear Differential Operators. Part I: Elementary Theory of Linear Differential Operators" (1967), George Harrap
  22. R. Paley, "Fourier Transforms in the Complex Domain Vol 19" (1934), Amer. Math. Soc. Colloquium Publ. Ser
  23. C. Shannon, "Communication in the presence of noise", Proc. I.R.E, 37, pp.10~21 (1949)
  24. L. O. Silva, "Bounded rank-one perturbations in sampling theory", J. Math. Anal. Appl, 345(2), pp.661~669 (2008)
  25. I. Stakgold, "Green’s Functions and Boundary Value Problems" (1987), John Wiley
  26. E. Whittaker, "On the functions which are represented by the expansion of the interpolation theory", Proc. Roy. Soc. Edinburgh Sec. A, 35, pp.181~194 (1915)
  27. A. I. Zayed, "Advances in Shannon’s Sampling Theory" (1993), CRC

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